C₃₇×#1939 #17990757

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1939

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator	C₂²	C₂²×C₈×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 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)(40,41)(43,45)(46,47,50,48,49,51,53,52);(39,41)(46,48,50,51,49,52,53,47);(42,43,44,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7118, C₃₇×#8843, C₃₇×#8844, …
maximal normal subgroup of	C₃₇×#7118, C₃₇×#8843, C₃₇×#8844, …
maximal quotient of	C₃₇×#9593, C₃₇×#9594, C₃₇×#9595, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 671);

C37×#1939 #17990757