C₃₇×#1768 #17990586

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#1768

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator	C₂²	C₂×C₄²×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; only the 168 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 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)(38,39,40,41)(42,43,45,44)(46,47)(48,51)(49,53)(50,52)(54,58)(55,57)(56,59)(60,61);(39,41)(46,48,49,54,50,55,56,60)(47,51,53,58,52,57,59,61);(42,44,45,43)(47,52)(51,57)(53,59)(58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1768, C₄×C₃₇×#424, C₃₇×#20427, …
maximal normal subgroup of	C₂×C₃₇×#1768, C₄×C₃₇×#424, C₃₇×#20427, …
maximal quotient of	C₃₇×#8264, C₃₇×#8265, C₃₇×#8270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 500);