C₃₇×#2756 #17991574

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#2756

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₃₇×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

484 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)(39,42)(40,44)(46,47,49,50)(48,51,52,53)(54,55,57,59)(56,60,61,58);(47,50)(48,52)(56,61)(58,60);(38,39,41,42)(40,43,44,45)(46,47)(48,51)(49,50)(52,53)(54,56,57,61)(55,58,59,60);(38,40)(39,43)(41,44)(42,45)(46,48,49,52)(47,51,50,53)(54,55)(56,58)(57,59)(60,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36758, C₃₇×#36768, C₃₇×#36774, …
maximal normal subgroup of	C₃₇×#36758, C₃₇×#36768, C₃₇×#36774, …
maximal quotient of	C₃₇×#14379, C₃₇×#14396, C₃₇×#14397, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1488);

C37×#2756 #17991574