C₃₇×#2412 #17991230

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2412

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂×#120×C₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

814 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)(42,43,44,45)(46,47)(48,49)(50,51)(52,53);(39,41)(47,51)(48,52);(38,39)(40,41)(42,43)(44,45)(46,48,50,52)(47,49,51,53);(46,49)(47,52)(48,51)(50,53)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#24405, C₃₇×#25565, C₂×C₃₇×#2412, …
maximal normal subgroup of	C₃₇×#24405, C₃₇×#25565, C₂×C₃₇×#2412, …
maximal quotient of	C₃₇×#13869, C₃₇×#13877, C₃₇×#13972, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1144);

C37×#2412 #17991230