C₂₉×D₂₃ #13050669

order	1334
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂×C₂₉)

Splittings

Fitting, socle, Hall	C₂₃×C₂₉ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₃×C₂₉	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 667

A minimal faithful permutation representation — 2 generators on 52 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52);(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₃×D₂₉, C₂×C₂₉×D₂₃, C₃×C₂₉×D₂₃, …
maximal normal subgroup of	D₂₃×D₂₉, C₂×C₂₉×D₂₃, C₃×C₂₉×D₂₃, …
maximal quotient of	C₂₉×Dic₂₃, C₂×C₂₉×D₂₃, C₃×C₂₉×D₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1334, 1);

C29×D23 #13050669