C₂₉×#2243 #16815957

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₉×#2243

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂×D₈×C₂₉	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

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

normal subgroups only

This group has 142 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)(40,49)(41,46)(42,45)(43,51)(44,48)(47,50)(52,53);(31,34)(35,37)(38,39,42,46,43,47,49,53,44,48,52,40,50,51,41,45);(30,32,33,36)(31,35,34,37)(38,40,41,48,50,53,52,47,44,46,49,39,43,45,42,51)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12376, C₂₉×#12377, C₂₉×#12378, …
maximal normal subgroup of	C₂₉×#12376, C₂₉×#12377, C₂₉×#12378, …
maximal quotient of	C₂₉×#12890, C₂₉×#13149, C₂₉×#13150, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 975);