Finite Group Databasebeta

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D5×C23×C13⋊C9 #41002094

order26910
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productD5×C23×C13⋊C9
unambiguous semidirect productC5⋊(C2×C23×C13⋊C9)
unambiguous semidirect product(D5×C13)⋊(C9×C23)
unambiguous semidirect product(D5×C13×C23)⋊C9

Splittings

derived, HallC5×C13 ⋊ C2×C9×C23
HallC5×C23×C13⋊C9 ⋊ C2
HallD5×C13×C23 ⋊ C9
HallC5×C13×C23 ⋊ C2×C9
HallC5×C13⋊C9 ⋊ C2×C23
HallC13×C23 ⋊ C9×D5
HallD5×C13 ⋊ C9×C23
HallC5×C23 ⋊ C2×C13⋊C9
SylowC13 ⋊ C9×D5×C23
SylowC5 ⋊ C2×C23×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C23D5×C13⋊C3
commutator, hypocenterC5×C13C2×C9×C23
FrattiniC3D5×C23×C13⋊C3
Fitting, socleC3×C5×C13×C23C2×C3
prime radicalC3×D5×C13×C23C3
cosocleC3×C5×C13C2×C3×C23
LCSG ▷ C5×C13
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 21);