C₂₉×#3026 #16816740

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#3026

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂⁴×C₂₉ ◁ G

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

normal subgroups only

This group has 800 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)(32,35)(33,36)(34,37)(38,44)(39,42)(40,43)(41,45);(30,32)(31,35)(33,38)(34,39)(36,41)(37,42)(40,45)(43,44);(30,33)(31,36)(32,38)(34,40)(35,41)(37,43)(39,45)(42,44);(31,37)(35,42)(36,43)(41,44)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#23895, C₂₉×#23896, C₂₉×#23996, …
maximal normal subgroup of	C₂₉×#23895, C₂₉×#23896, C₂₉×#23996, …
maximal quotient of	C₂₉×#18284, C₂₉×#18285, C₂₉×#18286, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1758);