C₃₇×#3368 #17992186

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3368

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×Q₈×C₃₇ ◁ G

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 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)(39,42)(43,44)(47,50)(48,52)(51,53);(38,39,41,42)(40,44,45,43)(47,51)(50,53);(46,47,49,51)(48,53,52,50);(38,40,41,45)(39,43,42,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#19795, C₃₇×#19799, C₃₇×#19843, …
maximal normal subgroup of	C₃₇×#19795, C₃₇×#19799, C₃₇×#19843, …
maximal quotient of	C₃₇×#22524, C₃₇×#22545, C₃₇×#22742, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2100);

C37×#3368 #17992186