C₃₇×#1384 #17990202

order	4736
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄²×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#1384

Subgroups

	subgroup	G/H
center	C₄×C₃₇	#106
commutator	C₈	C₄²×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂×C₃₇	#340
prime radical	C₂³×C₃₇	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(40,50,52,64)(41,47)(42,57)(43,59)(44,49)(45,51,60,65)(46,55)(48,58)(53,68,66,62)(54,69,67,61)(56,63);(38,40,42,53,58,67,56,65,44,52,55,66,43,54,41,51)(39,45,47,61,59,68,46,50,49,60,63,69,48,62,57,64)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7422, C₃₇×#7423, C₂×C₃₇×#1384, …
maximal normal subgroup of	C₃₇×#7422, C₃₇×#7423, C₂×C₃₇×#1384, …
maximal quotient of	C₃₇×#7157, C₃₇×#7174, C₃₇×#7218, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 116);

C37×#1384 #17990202