Finite Group Databasebeta

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C5×C11×AGL(1,𝔽23) #42123700

order27830
automorphism?
homologyAbelianization (H1) = C2×C5×C112 · Schur multiplier (H2) = C11

Aliases

direct productC5×C11×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C5×C112)
unambiguous semidirect product(C5×D23)⋊C112
unambiguous semidirect product(C23⋊C11)⋊(C2×C5×C11)
unambiguous semidirect product(C5×C11×D23)⋊C11

Splittings

Fitting, socleC5×C11×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C5×C112
HallC5×C11×C23⋊C11 ⋊ C2
HallC11×C23⋊C11 ⋊ C2×C5
HallC5×D23 ⋊ C112
HallC5×C23 ⋊ C2×C112
HallD23 ⋊ C5×C112

Subgroups

subgroupG/H
center, hypercenterC5×C11AGL(1,𝔽23)
commutator, cosocle, hypocenterC23C2×C5×C112
FrattiniC1G
Fitting, socleC5×C11×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C5×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1265

Conjugacy classes & character table

1265 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27830, 22);