C₃₇×#1839 #17990657

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

Aliases

direct product

C₃₇×#1839

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 61 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)(40,45)(41,43)(42,44)(46,47)(48,50)(49,51)(52,53)(54,55,56,58,57,59,60,61);(38,40,42,41)(39,43,44,45)(46,48,49,52)(47,50,51,53);(38,41,42,40)(39,43,44,45)(47,51)(50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7019, C₃₇×#7023, C₃₇×#7041, …
maximal normal subgroup of	C₃₇×#7019, C₃₇×#7023, C₃₇×#7041, …
maximal quotient of	C₃₇×#8800, C₃₇×#8801, C₃₇×#10795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 571);

C37×#1839 #17990657