C₂₉×#2216 #16815930

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2216

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂³×C₂₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

154 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 65
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 65 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)(32,33)(34,35,39,43)(36,44,48,60)(37,49,51,64)(38,52,50,42)(40,53,55,46)(41,56,57,45)(47,63,62,59)(54,61,58,65);(34,36,45,61,38,47,51,53,39,48,56,65,50,62,37,46)(35,40,49,59,42,54,57,60,43,55,64,63,52,58,41,44);(31,33)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7419, C₂₉×#7421, C₂₉×#13664, …
maximal normal subgroup of	C₂₉×#7419, C₂₉×#7421, C₂₉×#13664, …
maximal quotient of	C₂₉×#12431, C₂₉×#12440, C₂₉×#12452, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 948);