C₃₇×#3444 #17992262

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3444

Subgroups

	subgroup	G/H
center	C₄²×C₃₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₃₇ ◁ G

1212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(40,43)(41,42)(44,45)(46,47)(48,51)(49,50)(52,53);(39,42)(43,45);(47,50)(51,53);(46,48,49,52)(47,51,50,53);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12719, C₃₇×#17458, C₃₇×#17462, …
maximal normal subgroup of	C₃₇×#12719, C₃₇×#17458, C₃₇×#17462, …
maximal quotient of	C₃₇×#34012, C₃₇×#34026, C₄×C₃₇×#525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2176);

C37×#3444 #17992262