C₂₉×#2236 #16815950

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#2236

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

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

normal subgroups only

This group has 140 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)(41,44,47,51)(42,50,48,46)(45,53,52,49);(31,34)(35,37)(39,43)(44,51)(45,52)(46,50);(30,32,33,36)(31,35,34,37)(39,44)(41,49)(42,48)(43,51)(45,46)(47,53)(50,52)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12282, C₂₉×#12283, C₂₉×#12286, …
maximal normal subgroup of	C₂₉×#12282, C₂₉×#12283, C₂₉×#12286, …
maximal quotient of	C₂₉×#12867, C₂₉×#12919, C₂₉×#12993, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 968);