C₃₇×#2345 #17991163

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2345

Subgroups

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

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 57 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)(38,39,40,41)(42,43,46,45)(44,48,49,47)(51,54)(55,56);(43,45)(47,48)(50,51,53,54)(52,56,57,55);(42,44)(43,47)(45,48)(46,49);(42,45,46,43)(44,48,49,47)(50,52,53,57)(51,55,54,56)

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9257, C₃₇×#9261, C₃₇×#22513, …
maximal normal subgroup of	C₃₇×#9257, C₃₇×#9261, C₃₇×#22513, …
maximal quotient of	C₂²⋊C₄×C₄⋊C₄×C₃₇, C₃₇×#13802, C₃₇×#13812, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1077);

C37×#2345 #17991163