Finite Group Databasebeta

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C5×D23×C13⋊C9 #41002091

order26910
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D23×C13⋊C9
unambiguous semidirect productC23⋊(C2×C5×C13⋊C9)
unambiguous semidirect product(C13×D23)⋊(C5×C9)
unambiguous semidirect product(C5×C13×D23)⋊C9

Splittings

derived, HallC13×C23 ⋊ C2×C5×C9
HallC5×C23×C13⋊C9 ⋊ C2
HallC5×C13×D23 ⋊ C9
HallC23×C13⋊C9 ⋊ C2×C5
HallC5×C13×C23 ⋊ C2×C9
HallC13×D23 ⋊ C5×C9
HallC5×C23 ⋊ C2×C13⋊C9
HallC5×C13 ⋊ C9×D23
SylowC23 ⋊ C2×C5×C13⋊C9
SylowC13 ⋊ C5×C9×D23

Subgroups

subgroupG/H
center, hypercenterC3×C5C13⋊C3×D23
commutator, hypocenterC13×C23C2×C5×C9
FrattiniC3C5×C13⋊C3×D23
Fitting, socleC3×C5×C13×C23C2×C3
prime radicalC3×C5×C13×D23C3
cosocleC3×C13×C23C2×C3×C5
LCSG ▷ C13×C23
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 18);