C₂₉×#1854 #16815568

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

Aliases

direct product

C₂₉×#1854

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂⁴×C₂₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 45 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)(34,35,37,36)(39,43)(40,41)(44,45);(34,36,37,35)(38,39)(40,43)(41,45)(42,44);(31,33)(38,40,42,41)(39,43,44,45)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₉×#1854, C₂₉×#20843, C₂₉×#20845, …
maximal normal subgroup of	C₂×C₂₉×#1854, C₂₉×#20843, C₂₉×#20845, …
maximal quotient of	C₂₉×#8831, C₂₉×#8834, C₂₉×#8855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 586);

C29×#1854 #16815568