C₃₇×#335 #14557000

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×#335

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	D₄
commutator	C₄	C₂×C₈×C₃₇
Frattini, cosocle	C₄²	C₂²×C₃₇
socle, prime radical	C₂²×C₃₇	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₄²×C₃₇ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 53 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)(39,42)(40,43)(44,45)(46,47,48,50,49,51,52,53);(38,39,43,45,41,44,40,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#1331, C₃₇×#1332, C₃₇×#1361, …
maximal normal subgroup of	C₃₇×#1331, C₃₇×#1332, C₃₇×#1361, …
maximal quotient of	C₃₇×#1277, C₃₇×#1370, C₃₇×#1371, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 16);

C37×#335 #14557000