C₂₉×#2213 #16815927

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2213

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 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 — 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)(31,34)(32,37)(33,35)(38,39)(40,45)(41,44)(42,43);(30,31,35,38,36,39,33,34)(32,37,43,45,41,44,40,42);(30,32)(31,37)(33,40)(34,42)(35,43)(36,41)(38,45)(39,44)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12310, C₂₉×#12311, C₂₉×#12314, …
maximal normal subgroup of	C₂₉×#12310, C₂₉×#12311, C₂₉×#12314, …
maximal quotient of	C₂₉×#12418, C₂₉×#12419, C₂₉×#12424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 945);