Harada-Norton group

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This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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Definition

The Harada-Norton group, denoted HN, is one of the 26 sporadic simple groups that occurs in the classification of finite simple groups.

Arithmetic functions

Function Value Similar groups Explanation for function value
order (number of elements, equivalently, cardinality or size of underlying set) 273030912000000 groups with same order
number of conjugacy classes 54 groups with same order and number of conjugacy classes | groups with same number of conjugacy classes

Linear representation theory

Further information: linear representation theory of Harada-Norton group

Item Value
degrees of irreducible representations over a splitting field (such as \overline{\mathbb{Q}} or \mathbb{C}) 1, 133 (2 times), 760, 3344, 8778 (2 times), 8910, 9405, 16929, 35112 (2 times), 65835 (2 times), 69255 (2 times), 214016, 267520, 270864, 365750, 374528 (2 times), 406296, 653125, 656250 (2 times), 718200 (2 times), 1053360, 1066527 (2 times), 1185030 1354320, 1361920 (3 times), 1575936, 1625184, 2031480, 2375000, 2407680, 2661120, 2784375, 2985984, 3200000, 3424256, 3878280, 4156250, 4561920, 4809375, 5103000 (2 times), 5332635, 5878125
number: 54, quasirandom degree: 133, maximum: 5878125, sum of squares: 273030912000000

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