C₃₇×#446 #14557111

order	2368
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#446

Subgroups

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

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(40,45)(41,43)(42,44)(46,47,49,48,50,51,53,52);(38,40,42,41)(39,43,44,45);(38,41,42,40)(39,43,44,45)(46,48,49,51,50,52,53,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#1338, C₃₇×#1582, C₃₇×#1584, …
maximal normal subgroup of	C₃₇×#1338, C₃₇×#1582, C₃₇×#1584, …
maximal quotient of	C₃₇×#1770, C₃₇×#1771, C₃₇×#1916, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 127);

C37×#446 #14557111