C₃₇×#2158 #17990976

order	4736
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#2158

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	D₈
commutator	C₈	C₂²×C₄×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
socle	C₂²×C₃₇	C₂×D₈
prime radical	C₂³×C₃₇	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 73 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)(42,43)(44,53)(45,50)(46,60)(47,62)(48,52)(49,56)(51,54)(55,66)(57,72)(58,68)(59,65)(61,73)(63,70)(64,71)(67,69);(42,44,54,69,47,57,61,71,48,58,59,70,45,55,46,56)(43,49,60,66,50,63,65,68,52,64,73,72,62,67,51,53);(42,45,48,47)(43,50,52,62)(44,55,58,57)(46,59,61,54)(49,63,64,67)(51,60,65,73)(53,66,68,72)(56,70,71,69)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7473, C₃₇×#7475, C₃₇×#7477, …
maximal normal subgroup of	C₃₇×#7473, C₃₇×#7475, C₃₇×#7477, …
maximal quotient of	C₃₇×#12008, C₃₇×#12024, C₃₇×#12034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 890);

C37×#2158 #17990976