Finite Group Databasebeta

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C13×C5⋊AGL(1,𝔽23) #45659780

order32890
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊AGL(1,𝔽23)
unambiguous semidirect productC5⋊(C13×AGL(1,𝔽23))
unambiguous semidirect productD115⋊(C11×C13)
unambiguous semidirect product(C23⋊C11)⋊(D5×C13)
unambiguous semidirect product(C13×D115)⋊C11

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C2×C11×C13
HallC5×C13×C23⋊C11 ⋊ C2
HallC13×C23⋊C11 ⋊ D5
HallC13×D115 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×C13
HallC13×C23 ⋊ D5×C11
HallC23⋊C11 ⋊ D5×C13
HallD115 ⋊ C11×C13
HallC5×C13 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ D5×C11×C13
SylowC5 ⋊ C13×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC13C5⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC5×C23C2×C11×C13
FrattiniC1G
Fitting, socleC5×C13×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1495

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 23);