C₃₇×#2356 #17991174

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

Aliases

direct product

C₃₇×#2356

Subgroups

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

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8768, C₃₇×#8769, C₃₇×#8774, …
maximal normal subgroup of	C₃₇×#8768, C₃₇×#8769, C₃₇×#8774, …
maximal quotient of	C₃₇×#13804, C₃₇×#13806, C₃₇×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1088);

C37×#2356 #17991174