C₃₇×#3287 #17992105

order	4736
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3287

Subgroups

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

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(38,39)(40,41)(43,48)(44,46)(45,52)(49,53)(50,54)(56,57);(42,43,47,50)(44,48,46,54)(45,53,52,56)(49,55,57,51);(39,41)(42,44,47,46)(43,48,50,54)(45,51,52,55)(49,56,57,53);(42,45,47,52)(43,49,50,57)(44,51,46,55)(48,56,54,53)

Conjugacy classes & character table

1295 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12317, C₃₇×#12321, C₃₇×#12369, …
maximal normal subgroup of	C₃₇×#12317, C₃₇×#12321, C₃₇×#12369, …
maximal quotient of	C₃₇×#19867, C₃₇×#19868, C₃₇×#19869, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2019);

C37×#3287 #17992105