C₃₇×#350 #14557015

order	2368
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#350

Subgroups

	subgroup	G/H
center	C₈×C₃₇	D₄
commutator	C₄	C₂×C₈×C₃₇
Frattini, cosocle	C₂×C₈	C₂²×C₃₇
socle	C₂×C₃₇	C₂²⋊C₈
prime radical	#41×C₃₇	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇ ◁ C₂×C₈×C₃₇ ◁ G

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

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#350, C₃₇×#2117, C₃₇×#2170, …
maximal normal subgroup of	C₂×C₃₇×#350, C₃₇×#2117, C₃₇×#2170, …
maximal quotient of	C₃₇×#1315, C₃₇×#1323, C₃₇×D₄⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 31);

C37×#350 #14557015