Harada-Norton 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

External links

• HN on the Atlas of Finite Groups