C₃₇×#2311 #17991129

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₃₇×#2311

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂²×#41×C₃₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#10742, C₃₇×#10755, C₃₇×#10949, …
maximal normal subgroup of	C₃₇×#10742, C₃₇×#10755, C₃₇×#10949, …
maximal quotient of	C₃₇×#13777, C₃₇×#13784, C₃₇×#13785, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1043);

C37×#2311 #17991129