C₃₇×#3162 #17991980

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

Aliases

direct product

C₃₇×#3162

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂²×D₄
prime radical	C₂³×C₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

348 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)(48,55)(49,53)(50,59)(51,54)(52,58)(56,61)(57,60);(38,40,41,45)(39,42,43,44)(48,56)(52,60)(55,61)(57,58);(46,48,50,58,51,56,49,57)(47,52,53,55,54,60,59,61);(46,49,51,50)(47,53,54,59)(48,57,56,58)(52,55,60,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9006, C₃₇×#10036, C₃₇×#10037, …
maximal normal subgroup of	C₃₇×#9006, C₃₇×#10036, C₃₇×#10037, …
maximal quotient of	C₃₇×#20799, C₃₇×#21154, C₃₇×#21321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1894);

C37×#3162 #17991980