C₃₇×#1377 #17990195

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1377

Subgroups

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

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(42,43,44,48,45,49,51,55,46,47,50,53,52,54,56,57);(38,39,40,41)(43,47)(44,50)(49,54)(51,56)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7105, C₃₇×#7110, C₃₇×#7111, …
maximal normal subgroup of	C₃₇×#7105, C₃₇×#7110, C₃₇×#7111, …
maximal quotient of	C₃₇×#7139, C₃₇×#7143, C₃₇×#7146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 109);

C37×#1377 #17990195