# Suzuki sporadic group

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## Definition

The Suzuki sporadic group, denoted Suz, is one of the 26 sporadic simple groups that appear in the classification of finite simple groups. It has order:

$448345497600 = 2^{13} \cdot 3^7 \cdot 5^2 \cdot 7 \cdot 11 \cdot 13$

## Arithmetic functions

Function Value Similar groups Explanation for function value
order (number of elements, equivalently, cardinality or size of underlying set) 448345497600 groups with same order
number of conjugacy classes 43

## Linear representation theory

Further information: linear representation theory of Suzuki sporadic group

Item Value
degrees of irreducible representations over a splitting field (such as $\overline{\mathbb{Q}}$ or $\mathbb{C}$) 1, 143, 364, 780, 1001, 3432, 5005 (2 times), 5940, 10725, 12012, 14300, 15015 (2 times), 15795, 18954, 25025 (3 times), 40040, 50050 (2 times), 54054, 64064, 64350 (2 times), 66560, 75075, 79872, 88452, 93555 (2 times), 100100, 133056, 146432, 163800, 168960, 189540, 193050, 197120, 208494, 243243, 248832
number: 43, quasirandom degree: 143, maximum: 248832, sum of squares: 448345497600