C₃₇×#2176 #17990994

order	4736
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2176

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	C₂×D₈
commutator	C₈	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 73 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)(38,39,41,40)(42,43)(44,52)(45,56)(46,61)(47,49)(48,53)(50,59)(51,58)(54,72)(55,69)(57,67)(60,68)(62,66)(63,71)(64,73)(65,70);(42,44,47,55)(43,48,49,63)(45,57,60,73)(46,62,58,54)(50,66,65,72)(51,67,61,64)(52,68,69,56)(53,70,71,59);(38,40,41,39)(43,49)(48,63)(50,65)(51,61)(52,69)(56,68)(64,67)(66,72)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7391, C₃₇×#12066, C₃₇×#12079, …
maximal normal subgroup of	C₃₇×#7391, C₃₇×#12066, C₃₇×#12079, …
maximal quotient of	C₃₇×#12044, C₃₇×#12076, C₃₇×#12085, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 908);

C37×#2176 #17990994