C₃₇×#2177 #17990995

order	4736
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2177

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×D₈
commutator	C₈	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
prime radical	C₂×D₁₆×C₃₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(38,39,41,40)(42,43,45,48)(44,47,53,55)(46,54,52,50)(49,57,56,51);(43,47)(44,51)(46,52)(48,55)(49,50)(53,57)(54,56);(38,40,41,39)(43,48)(47,55)(49,56)(50,54)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7390, C₃₇×#12067, C₃₇×#12078, …
maximal normal subgroup of	C₃₇×#7390, C₃₇×#12067, C₃₇×#12078, …
maximal quotient of	C₃₇×#12045, C₃₇×#12073, C₃₇×#12086, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 909);

C37×#2177 #17990995