C₂₉×#2675 #16816389

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#2675

Subgroups

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

804 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 41
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 41 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)(35,37);(31,32)(39,41);(34,35)(36,37)(38,39)(40,41);(30,32,33,31)(34,35)(36,37)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12148, C₂₉×#12242, C₂₉×#36706, …
maximal normal subgroup of	C₂₉×#12148, C₂₉×#12242, C₂₉×#36706, …
maximal quotient of	C₂₉×#14361, C₂₉×#14402, C₂₉×#14521, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1407);