C₃₇×#504 #14557169

order	2368
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#504

Subgroups

	subgroup	G/H
center	C₁₆×C₃₇	C₂²
commutator	C₂	C₂²×C₈×C₃₇
Frattini, cosocle	C₈	C₂³×C₃₇
socle	C₂×C₃₇	C₂²×C₈
prime radical	#41×C₃₇	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₃₇ ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(38,39,41,45,42,46,51,57,43,47,52,58,53,59,63,67)(40,44,49,55,50,56,62,66,48,54,60,64,61,65,68,69);(38,40)(39,44)(41,49)(42,50)(43,48)(45,55)(46,56)(47,54)(51,62)(52,60)(53,61)(57,66)(58,64)(59,65)(63,68)(67,69);(40,48)(44,54)(49,60)(50,61)(55,64)(56,65)(62,68)(66,69)

Conjugacy classes & character table

1480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#1401, C₃₇×#2170, C₃₇×#2171, …
maximal normal subgroup of	C₃₇×#1401, C₃₇×#2170, C₃₇×#2171, …
maximal quotient of	C₃₇×#2108, C₃₇×#2113, C₃₇×#2151, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 185);

C37×#504 #14557169