C₃₇×#2710 #17991528

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#2710

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₃₇×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

548 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)(43,46)(44,48)(50,51,54,56)(52,57,53,55);(39,41)(43,46)(47,49)(50,52,54,53)(51,55,56,57);(38,39)(40,41)(42,43,45,46)(44,47,48,49)(50,53,54,52)(51,55,56,57);(42,44)(43,47)(45,48)(46,49)(50,51)(52,57)(53,55)(54,56)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#36739, C₃₇×#36743, C₃₇×#36766, …
maximal normal subgroup of	C₃₇×#36739, C₃₇×#36743, C₃₇×#36766, …
maximal quotient of	C₃₇×#14376, C₃₇×#14384, C₃₇×#14386, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1442);

C37×#2710 #17991528