Finite Group Databasebeta

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C5×C9×C13×D23 #41002076

order26910
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, SylowC23 ⋊ C2×C5×C9×C13
HallC9×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ C2×C9
HallC5×C9×C23 ⋊ C2×C13
HallC13×C23 ⋊ C2×C5×C9
HallC9×C23 ⋊ C2×C5×C13
HallC5×C23 ⋊ C2×C9×C13

Subgroups

subgroupG/H
center, hypercenterC5×C9×C13D23
commutator, hypocenterC23C2×C5×C9×C13
FrattiniC3C3×C5×C13×D23
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23C2×C3
prime radicalC3×C5×C13×D23C3
cosocleC3×C23C2×C3×C5×C13
LCSG ▷ C23
UCSC1 ◁ C5×C9×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

7605 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 3);