C₃₇×#2346 #17991164

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₃₇×#2346

Subgroups

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

504 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)(38,39,40,41)(42,43,46,45)(44,47,49,48)(51,52)(55,56);(43,45)(47,48)(50,51,54,52)(53,56,57,55);(42,44,46,49)(43,47,45,48)(50,52,54,51)(53,56,57,55);(42,45,46,43)(44,48,49,47)(50,53,54,57)(51,55,52,56)

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9363, C₃₇×#9367, C₃₇×#17605, …
maximal normal subgroup of	C₃₇×#9363, C₃₇×#9367, C₃₇×#17605, …
maximal quotient of	C₃₇×#13801, C₃₇×#13805, C₃₇×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1078);

C37×#2346 #17991164