C₃₇×#2571 #17991389

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2571

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

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

normal subgroups only

This group has 380 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)(38,39,42,40)(41,44,45,43)(47,49)(51,52)(54,55,58,61)(56,60,57,59);(39,40)(43,44)(46,47,50,49)(48,51,53,52)(54,56,58,57)(55,59,61,60);(38,40,42,39)(41,44,45,43)(46,48,50,53)(47,51,49,52)(54,55)(56,59)(57,60)(58,61);(38,41,42,45)(39,43,40,44)(46,49,50,47)(48,52,53,51)(54,57,58,56)(55,60,61,59)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#10351, C₃₇×#10352, C₃₇×#10353, …
maximal normal subgroup of	C₃₇×#10351, C₃₇×#10352, C₃₇×#10353, …
maximal quotient of	C₃₇×#13911, C₃₇×#13982, C₃₇×#14030, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1303);