Finite Group Databasebeta

← Prev (#13095004) Next (#13095006) →

C3⋊AGL(1,𝔽23) #13095005

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

Aliases

unambiguous semidirect productC3⋊AGL(1,𝔽23)
unambiguous semidirect productD69⋊C11
unambiguous semidirect product(C23⋊C11)⋊D3

Splittings

Fitting, socle, derived, HallC3×C23 ⋊ C2×C11
HallC3×C23⋊C11 ⋊ C2
HallC23⋊C11 ⋊ D3
HallD69 ⋊ C11
SylowC23 ⋊ D3×C11
SylowC3 ⋊ AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C23C2×C11
LCSG ▷ C3×C23
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

Polycyclic presentation:

2,11,3,23|c^a=c^2,d^a=d^22,d^b=d^3

Conjugacy classes & character table

36 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), C3×C3⋊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, 3);