C₃₇×#3164 #17991982

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3164

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂³×C₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ G

340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 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)(38,39,41,43)(40,44,45,42)(48,54)(49,55)(51,57)(53,58)(56,60)(59,61);(38,40,41,45)(39,42,43,44)(46,47)(48,51)(49,53)(50,52)(54,57)(55,58)(56,59)(60,61);(46,48,55,60,50,56,49,54)(47,51,58,61,52,59,53,57);(47,52)(51,59)(53,58)(57,61)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#13369, C₃₇×#13370, C₃₇×#13455, …
maximal normal subgroup of	C₃₇×#13369, C₃₇×#13370, C₃₇×#13455, …
maximal quotient of	C₃₇×#20803, C₃₇×#21156, C₃₇×#21158, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1896);

C37×#3164 #17991982