C₃₇×#2344 #17991162

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

Aliases

direct product

C₃₇×#2344

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

604 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)(38,39,41,40)(42,43,44,45)(48,52)(50,53);(39,40)(46,47,49,51)(48,50,52,53);(46,48)(47,50)(49,52)(51,53);(38,40,41,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9256, C₃₇×#9260, C₃₇×#22406, …
maximal normal subgroup of	C₃₇×#9256, C₃₇×#9260, C₃₇×#22406, …
maximal quotient of	C₃₇×#13799, C₂²⋊C₄×C₄⋊C₄×C₃₇, C₃₇×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1076);

C37×#2344 #17991162