C₃₇×#3009 #17991827

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#3009

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×H(5,𝔽₂)×C₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#13097, C₃₇×#13100, C₃₇×#23894, …
maximal normal subgroup of	C₃₇×#13097, C₃₇×#13100, C₃₇×#23894, …
maximal quotient of	C₃₇×#18225, C₃₇×#18233, C₃₇×#18241, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1741);

C37×#3009 #17991827