Finite Group Databasebeta

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C23×D715 #45659774

order32890
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D715
unambiguous semidirect productC5⋊(C23×D143)
unambiguous semidirect productC11⋊(C23×D65)
unambiguous semidirect productC13⋊(C23×D55)

Splittings

Fitting, socle, HallC5×C11×C13×C23 ⋊ C2
derived, HallC5×C11×C13 ⋊ C2×C23
HallC11×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ D11
HallC5×C11×C23 ⋊ D13
HallC13×C23 ⋊ D55
HallC11×C23 ⋊ D65
HallC11×C13 ⋊ D5×C23
HallC5×C23 ⋊ D143
HallC5×C13 ⋊ D11×C23
HallC5×C11 ⋊ C23×D13
SylowC13 ⋊ C23×D55
SylowC11 ⋊ C23×D65
SylowC5 ⋊ C23×D143

Subgroups

subgroupG/H
center, hypercenterC23D715
commutator, cosocle, hypocenterC5×C11×C13C2×C23
FrattiniC1G
Fitting, socleC5×C11×C13×C23C2
LCSG ▷ C5×C11×C13
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16445

Conjugacy classes & character table

8257 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 17);