C₃₇×#2850 #17991668

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₇×#2850

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂×#121×C₃₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

696 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)(43,44)(47,50)(51,53);(42,43,45,44)(46,47)(48,51)(49,50)(52,53);(42,44,45,43)(46,48,49,52)(47,51,50,53);(38,39)(40,41)(46,47)(48,51)(49,50)(52,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7670, C₃₇×#7690, C₃₇×#7710, …
maximal normal subgroup of	C₃₇×#7670, C₃₇×#7690, C₃₇×#7710, …
maximal quotient of	C₃₇×#14682, C₃₇×#14696, C₃₇×#14698, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1582);

C37×#2850 #17991668