C₃₇×#1380 #17990198

order	4736
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄²×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1380

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	D₈
commutator	C₈	C₄²×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 2 generators on 61 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)(42,43,44,45)(47,52)(48,56)(49,58)(50,57)(53,54)(55,61)(59,60);(39,41)(46,47,49,53,50,54,48,52,51,55,56,60,57,59,58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7418, C₃₇×#7419, C₂×C₃₇×#1380, …
maximal normal subgroup of	C₃₇×#7418, C₃₇×#7419, C₂×C₃₇×#1380, …
maximal quotient of	C₃₇×#7154, C₃₇×#7171, C₃₇×#7217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 112);

C37×#1380 #17990198