C₃₇×#3333 #17992151

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3333

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×D₄×C₃₇ ◁ G

398 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)(46,47,51,55)(48,56,57,61)(49,54,50,53)(52,59,60,58);(38,40)(39,42)(41,45)(43,44)(48,57)(52,60)(56,61)(58,59);(46,48,51,57)(47,52,55,60)(49,58,50,59)(53,56,54,61);(40,45)(42,44)(46,49,51,50)(47,53,55,54)(48,58,57,59)(52,56,60,61)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#19781, C₃₇×#19785, C₃₇×#19829, …
maximal normal subgroup of	C₃₇×#19781, C₃₇×#19785, C₃₇×#19829, …
maximal quotient of	C₃₇×#22432, C₃₇×#22502, C₃₇×#22579, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2065);

C37×#3333 #17992151