C₃₇×#2916 #17991734

order	4736
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2916

Subgroups

	subgroup	G/H
center	C₄×C₃₇	C₂²×D₄
commutator	C₄	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂×C₃₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 69 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)(38,39,43,47,44,48,42,57)(40,49,52,59,53,63,51,45)(41,46,56,61,54,60,55,67)(50,62,66,68,64,69,65,58);(38,40,42,51,44,53,43,52)(39,45,47,49,48,59,57,63)(41,50,55,65,54,64,56,66)(46,58,61,62,60,68,67,69);(38,41)(39,46)(40,50)(42,55)(43,56)(44,54)(45,58)(47,61)(48,60)(49,62)(51,65)(52,66)(53,64)(57,67)(59,68)(63,69);(41,54)(46,60)(50,64)(55,56)(58,68)(61,67)(62,69)(65,66)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12877, C₃₇×#12878, C₃₇×#12927, …
maximal normal subgroup of	C₃₇×#12877, C₃₇×#12878, C₃₇×#12927, …
maximal quotient of	C₃₇×#17788, C₃₇×#17789, C₃₇×#17798, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1648);

C37×#2916 #17991734