C₂₉×#3038 #16816752

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#3038

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

584 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 208 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 — 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)(31,33)(35,39)(36,37)(40,41);(30,31,32,33);(34,35)(36,39)(37,41)(38,40);(34,36,38,37)(35,39,40,41)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#9173, C₂₉×#9174, C₂₉×#9318, …
maximal normal subgroup of	C₂₉×#9173, C₂₉×#9174, C₂₉×#9318, …
maximal quotient of	C₂₉×#19266, C₂₉×#19267, C₂₉×#19268, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1770);