C₃₇×#2935 #17991753

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2935

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₃₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

492 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)(42,43,47,50,46,49,55,57)(44,51,53,54,52,48,56,45);(39,41)(42,44)(43,48)(45,50)(46,52)(47,53)(49,51)(54,57)(55,56);(42,45,47,51,46,54,55,48)(43,44,50,53,49,52,57,56);(44,52)(45,54)(48,51)(53,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8930, C₃₇×#8932, C₃₇×#9053, …
maximal normal subgroup of	C₃₇×#8930, C₃₇×#8932, C₃₇×#9053, …
maximal quotient of	C₃₇×#18066, C₃₇×#18067, C₃₇×#18068, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1667);

C37×#2935 #17991753