C₃₇×#2772 #17991590

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2772

Subgroups

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

378 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)(40,44)(41,42)(43,45)(47,48)(51,52)(54,55,58,61)(56,59,60,57);(39,42)(40,45)(46,47,50,48)(49,52,53,51)(54,56,58,60)(55,59,61,57);(38,39)(40,43)(41,42)(44,45)(46,48,50,47)(49,52,53,51)(54,57,58,59)(55,60,61,56);(38,40,41,45)(39,43,42,44)(46,49,50,53)(47,51,48,52)(54,55)(56,59)(57,60)(58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36760, C₃₇×#36763, C₃₇×#36769, …
maximal normal subgroup of	C₃₇×#36760, C₃₇×#36763, C₃₇×#36769, …
maximal quotient of	C₃₇×#14385, C₃₇×#14412, C₃₇×#14434, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1504);

C37×#2772 #17991590