C₂₉×#1859 #16815573

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1859

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

302 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 928

A minimal faithful permutation representation — 3 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)(30,31,33,32)(35,39)(36,37)(40,41);(30,32,33,31)(34,35)(36,41)(37,39)(38,40);(34,35)(36,39)(37,41)(38,40)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1859, C₂₉×#20863, C₂₉×#20864, …
maximal normal subgroup of	C₂×C₂₉×#1859, C₂₉×#20863, C₂₉×#20864, …
maximal quotient of	C₂₉×#8839, C₂₉×#8841, C₂₉×#8866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 591);