C₂₉×#2232 #16815946

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2232

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂₉×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

150 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 53 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)(33,34)(36,37)(38,39)(40,43)(41,50)(42,46)(44,47)(45,48)(49,52)(51,53);(31,34)(35,37);(30,32,33,36)(31,35,34,37)(39,43)(40,47)(41,48)(44,45)(46,52)(49,53)(50,51)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12278, C₂₉×#12280, C₂₉×#12284, …
maximal normal subgroup of	C₂₉×#12278, C₂₉×#12280, C₂₉×#12284, …
maximal quotient of	C₂₉×#12866, C₂₉×#12919, C₂₉×#12991, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 964);