C₃₇×#1835 #17990653

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

Aliases

direct product

C₃₇×#1835

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 65 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)(44,47)(45,46)(48,49)(50,51)(52,60)(53,56)(54,64)(55,59)(57,62)(58,61)(63,65);(43,46)(47,49)(50,52,61,63,55,62,54,53)(51,56,64,57,59,65,58,60);(42,44,45,48)(43,47,46,49)(50,53,54,62,55,63,61,52)(51,57,58,56,59,60,64,65)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7218, C₃₇×#7221, C₃₇×#7366, …
maximal normal subgroup of	C₃₇×#7218, C₃₇×#7221, C₃₇×#7366, …
maximal quotient of	C₃₇×#8785, C₃₇×#8788, C₃₇×#8791, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 567);

C37×#1835 #17990653