C₃₇×#2906 #17991724

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

Aliases

direct product

C₃₇×#2906

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	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

484 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)(39,41)(42,43,45,48,46,49,52,55)(44,47,51,54,50,53,56,57);(38,39,40,41);(42,44)(43,47)(45,51)(46,50)(48,54)(49,53)(52,56)(55,57);(44,50)(47,53)(51,56)(54,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8902, C₃₇×#8904, C₃₇×#8993, …
maximal normal subgroup of	C₃₇×#8902, C₃₇×#8904, C₃₇×#8993, …
maximal quotient of	C₃₇×#17826, C₃₇×#17827, C₃₇×#17828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1638);

C37×#2906 #17991724