C₂₉×#2234 #16815948

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₉×#2234

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

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

normal subgroups only

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

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2234, C₂₉×#33645, C₂₉×#33647, …
maximal normal subgroup of	C₂×C₂₉×#2234, C₂₉×#33645, C₂₉×#33647, …
maximal quotient of	C₂₉×#12868, C₂₉×#12921, C₂₉×#12992, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 966);