Finite Group Databasebeta

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C23×D585 #41002089

order26910
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D585
unambiguous semidirect productC5⋊(C23×D117)
unambiguous semidirect productC9⋊(C23×D65)
unambiguous semidirect productC13⋊(C23×D45)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC5×C9×C13 ⋊ C2×C23
HallC9×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ D9
HallC5×C9×C23 ⋊ D13
HallC13×C23 ⋊ D45
HallC9×C23 ⋊ D65
HallC9×C13 ⋊ D5×C23
HallC5×C23 ⋊ D117
HallC5×C13 ⋊ D9×C23
HallC5×C9 ⋊ C23×D13
SylowC13 ⋊ C23×D45
SylowC9 ⋊ C23×D65
SylowC5 ⋊ C23×D117

Subgroups

subgroupG/H
center, hypercenterC23D585
commutator, cosocle, hypocenterC5×C9×C13C2×C23
FrattiniC3C23×D195
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 16);