C₃₇×#533 #14557198

order	2368
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#533

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂⁴
prime radical	C₂³×C₃₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 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)(40,43)(41,42)(44,45)(46,47,49,51)(48,52,53,50);(39,42)(43,45);(46,48,49,53)(47,50,51,52);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#1481, C₃₇×#1485, C₃₇×#1493, …
maximal normal subgroup of	C₃₇×#1481, C₃₇×#1485, C₃₇×#1493, …
maximal quotient of	C₃₇×#2285, C₃₇×#2295, C₃₇×#2296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 214);

C37×#533 #14557198