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C5×C13⋊AGL(1,𝔽23) #45659778

order32890
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊AGL(1,𝔽23)
unambiguous semidirect productC13⋊(C5×AGL(1,𝔽23))
unambiguous semidirect product(C23⋊C11)⋊(C5×D13)
unambiguous semidirect productD299⋊(C5×C11)
unambiguous semidirect product(C5×D299)⋊C11

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C11
derived, HallC13×C23 ⋊ C2×C5×C11
HallC5×C13×C23⋊C11 ⋊ C2
HallC13×C23⋊C11 ⋊ C2×C5
HallC5×D299 ⋊ C11
HallC5×C23⋊C11 ⋊ D13
HallD299 ⋊ C5×C11
HallC23⋊C11 ⋊ C5×D13
HallC5×C23 ⋊ C11×D13
HallC5×C13 ⋊ AGL(1,𝔽23)
SylowC23 ⋊ C5×C11×D13
SylowC13 ⋊ C5×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC5C13⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC13×C23C2×C5×C11
FrattiniC1G
Fitting, socleC5×C13×C23C2×C11
LCSG ▷ C13×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1495

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 21);