O'Nan group

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VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
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Definition

Th O'Nan group, denoted ON, is one of the 26 sporadic simple groups that appear in the classification of finite simple groups. It has order:

$460815505920=2^{9}\cdot 3^{4}\cdot 5\cdot 7^{3}\cdot 11\cdot 19\cdot 31$

Arithmetic functions

Function	Value	Similar groups	Explanation for function value
order (number of elements, equivalently, cardinality or size of underlying set)	460815505920	groups with same order
number of conjugacy classes	30

Linear representation theory

Further information: linear representation theory of O'Nan group

Item	Value
degrees of irreducible representations over a splitting field (such as ${\overline {\mathbb {Q} }}$ or $\mathbb {C}$)	1, 10944, 13376 (2 times), 25916 (2 times), 26752, 32395 (2 times), 37696, 52668, 53811 (3 times), 58653, 64790 (2 times), 85064, 116963, 143374, 169290 (2 times), 175616 (2 times), 175770, 207360 (3 times), 234080 (2 times) number: 30, quasirandom degree: 10944, maximum: 234080, sum of squares: 460815505920

External links

• ON on the Atlas of Finite Groups