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C2×C52×C23×C31 #49087154

order35650
nilpotency class1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C5

Aliases

abelianC2×C52×C23×C31

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 35650

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2)(3,4,5,6,7)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35)(36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(8,9,10,11,12)

Conjugacy classes & character table

35650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35650, 13);