C₃₇×#2083 #17990901

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2083

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

230 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(44,49)(45,47)(46,48);(42,44,46,45)(43,47,48,49)(50,51)(52,54)(53,56)(55,57);(39,41)(42,45,46,44)(43,47,48,49)(51,54)(52,57)(55,56)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7788, C₃₇×#7789, C₃₇×#7790, …
maximal normal subgroup of	C₃₇×#7788, C₃₇×#7789, C₃₇×#7790, …
maximal quotient of	C₃₇×#10649, C₃₇×#10650, C₃₇×#10653, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 815);