C₃₇×#2863 #17991681

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2863

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

408 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 216 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 — 4 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)(38,39,43,42)(40,45,41,44)(46,47,50,53)(48,51,52,49)(56,60)(58,61);(38,40,43,41)(39,44,42,45)(46,48,50,52)(47,51,53,49)(54,55,57,59)(56,58,60,61);(38,41,43,40)(39,45,42,44)(46,49,50,51)(47,52,53,48);(38,42,43,39)(40,45,41,44)(46,47)(48,51)(49,52)(50,53)(54,56)(55,58)(57,60)(59,61)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7669, C₃₇×#7673, C₃₇×#7689, …
maximal normal subgroup of	C₃₇×#7669, C₃₇×#7673, C₃₇×#7689, …
maximal quotient of	C₃₇×#14688, C₃₇×#14699, C₃₇×#14703, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1595);