C₃₇×#349 #14557014

order	2368
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#349

Subgroups

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

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

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)(38,39,40,44,41,45,47,51,42,43,46,49,48,50,52,53);(39,43)(40,46)(45,50)(47,52)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#1320, C₃₇×#1321, C₃₇×#1327, …
maximal normal subgroup of	C₃₇×#1320, C₃₇×#1321, C₃₇×#1327, …
maximal quotient of	C₃₇×#1314, C₃₇×#1322, C₃₇×#1330, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 30);

C37×#349 #14557014

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₃₇×#349 #14557014