C₃₇×#1829 #17990647

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1829

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	#381
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

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

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12725, C₃₇×#12726, C₂×C₃₇×#1829, …
maximal normal subgroup of	C₃₇×#12725, C₃₇×#12726, C₂×C₃₇×#1829, …
maximal quotient of	C₃₇×#8734, C₃₇×#8736, C₃₇×#8751, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 561);

C37×#1829 #17990647