# O'Nan group

From Groupprops

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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:

## 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 or ) | 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 |