C₂₉×#2733 #16816447

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₂₉×#2733

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

592 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 49
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 49 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)(34,35,38,36)(37,40,41,39)(43,44)(47,48);(31,33)(35,36)(37,41)(42,43,46,44)(45,48,49,47);(30,31)(32,33)(34,36,38,35)(37,40,41,39)(42,44,46,43)(45,48,49,47);(34,37,38,41)(35,39,36,40)(42,45)(43,47)(44,48)(46,49)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#7742, C₂₉×#7758, C₂₉×#7781, …
maximal normal subgroup of	C₂₉×#7742, C₂₉×#7758, C₂₉×#7781, …
maximal quotient of	C₂₉×#14399, C₂₉×#14445, C₂₉×#14467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1465);