C₂₉×#3019 #16816733

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#3019

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

762 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 212 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) = 45
transitive degree	μ_t(G) = 464

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

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#23872, C₂₉×#23873, C₂₉×#23892, …
maximal normal subgroup of	C₂₉×#23872, C₂₉×#23873, C₂₉×#23892, …
maximal quotient of	C₂₉×#18132, C₂₉×#18133, C₂₉×#18137, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1751);