C₂₉×C₂₃⋊AGL(1,𝔽₅) #27211112

order	13340
isoclinism	isoclinic class of C₂₃⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×C₂₃⋊AGL(1,𝔽₅)
unambiguous semidirect product	C₂₃⋊(AGL(1,𝔽₅)×C₂₉)

Splittings

Fitting, socle, Hall	C₅×C₂₃×C₂₉ ⋊ C₄
derived, Hall	C₅×C₂₃ ⋊ C₄×C₂₉
Hall	C₂₃×C₂₉ ⋊ AGL(1,𝔽₅)
Hall	C₅×C₂₉ ⋊ Dic₂₃
Sylow	C₂₃ ⋊ AGL(1,𝔽₅)×C₂₉
Sylow	C₅ ⋊ C₂₉×Dic₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	C₂₃⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₂₃	C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₂₃×C₂₉	C₄
prime radical	D₅×C₂₃×C₂₉	C₂
cosocle	D₅×C₂₃	C₂×C₂₉
LCS	G ▷ C₅×C₂₃
UCS	C₁ ◁ C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 3335

A minimal faithful permutation representation — 2 generators on 57 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,28,26,27)

Conjugacy classes & character table

1421 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13340, 17);

C29×C23⋊AGL(1,𝔽5) #27211112