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C3×AGL(1,𝔽23) #13095003

order1518
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C3×C11)
unambiguous semidirect product(C3×D23)⋊C11
unambiguous semidirect product(C23⋊C11)⋊(C2×C3)

Splittings

Fitting, socle, HallC3×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C3×C11
HallC3×C23⋊C11 ⋊ C2
HallC23⋊C11 ⋊ C2×C3
HallC3×D23 ⋊ C11
HallD23 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C2×C3×C11
FrattiniC1G
Fitting, socleC3×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C3

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 69

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3)(5,8,9,16,17,24,19,20,10,21,22,6,7,11,12,23,18,13,25,14,15,26);(4,5,7,10,9,13,15,23,12,18,20,26,22,25,24,16,17,21,19,11,14,8,6)

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽23), C2×C3×AGL(1,𝔽23), C9×AGL(1,𝔽23), …
maximal normal subgroup ofD3×AGL(1,𝔽23), C2×C3×AGL(1,𝔽23), C9×AGL(1,𝔽23), …
maximal quotient ofC3×Dic23⋊C11, C2×C3×AGL(1,𝔽23), C9×AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1518, 1);