C₂₉×#2230 #16815944

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2230
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#2230

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#476
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

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

normal subgroups only

This group has 126 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)(32,40,42,37)(33,35)(38,39)(41,43,44,45);(30,31,33,34,36,39,35,38)(32,37,41,43,42,40,44,45);(30,32)(31,37)(33,41)(34,43)(35,44)(36,42)(38,45)(39,40)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12364, C₂₉×#12365, C₂₉×#12366, …
maximal normal subgroup of	C₂₉×#12364, C₂₉×#12365, C₂₉×#12366, …
maximal quotient of	C₂₉×#12823, C₂₉×#12950, C₂₉×#13116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 962);