C₃₇×#1822 #17990640

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1822

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
prime radical	C₂⁴×C₃₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 3 generators on 61 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)(40,43)(41,42)(44,45)(46,47,49,53,50,52,56,59)(48,51,54,58,55,57,60,61);(39,42)(43,45)(46,48,50,55)(47,51,52,57)(49,54,56,60)(53,58,59,61);(38,40,41,44)(39,43,42,45)(47,52)(49,56)(51,57)(54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7216, C₃₇×#7350, C₃₇×#7351, …
maximal normal subgroup of	C₃₇×#7216, C₃₇×#7350, C₃₇×#7351, …
maximal quotient of	C₃₇×#8699, C₃₇×#8700, C₃₇×#8702, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 554);

C37×#1822 #17990640