Finite Group Databasebeta

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C2×C5×C23×C13⋊C9 #41002075

order26910
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C23×C13⋊C9
unambiguous semidirect product(C2×C13)⋊(C5×C9×C23)
unambiguous semidirect product(C2×C5×C13)⋊(C9×C23)
unambiguous semidirect product(C2×C13×C23)⋊(C5×C9)
unambiguous semidirect product(C2×C5×C13×C23)⋊C9

Splittings

derived, SylowC13 ⋊ C2×C5×C9×C23
HallC2×C5×C13×C23 ⋊ C9
HallC5×C13×C23 ⋊ C2×C9
HallC2×C13×C23 ⋊ C5×C9
HallC13×C23 ⋊ C2×C5×C9
HallC2×C5×C13 ⋊ C9×C23
HallC5×C13 ⋊ C2×C9×C23
HallC2×C13 ⋊ C5×C9×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C23C13⋊C3
commutator, hypocenterC13C2×C5×C9×C23
FrattiniC3C2×C5×C23×C13⋊C3
Fitting, socle, prime radicalC2×C3×C5×C13×C23C3
cosocleC3×C13C2×C3×C5×C23
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26910

Conjugacy classes & character table

4830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 2);