C₃₇×#2855 #17991673

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

Aliases

direct product

C₃₇×#2855

Subgroups

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

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 57 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)(42,43,45,47)(44,48,49,46)(50,51,54,53)(52,56,57,55);(42,43)(44,46)(45,47)(48,49)(50,52,54,57)(51,55,53,56);(42,43)(44,46)(45,47)(48,49);(38,39)(40,41)(42,44,45,49)(43,46,47,48)(50,53,54,51)(52,56,57,55)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7655, C₃₇×#7661, C₃₇×#7675, …
maximal normal subgroup of	C₃₇×#7655, C₃₇×#7661, C₃₇×#7675, …
maximal quotient of	C₃₇×#14685, C₃₇×#14695, C₃₇×#14697, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1587);

C37×#2855 #17991673