C₃₇×#3541 #17992359

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3541

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 generators on 61 points:

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

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#61610, C₃₇×#61612, C₃₇×#61613, …
maximal normal subgroup of	C₃₇×#61610, C₃₇×#61612, C₃₇×#61613, …
maximal quotient of	C₃₇×#34362, C₃₇×#34370, C₃₇×#34404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2273);

C37×#3541 #17992359