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C13×C23×D55 #45659772

order32890
automorphism?
homologyAbelianization (H1) = C2×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productC13×C23×D55
unambiguous semidirect productC5⋊(C13×D11×C23)
unambiguous semidirect productC11⋊(D5×C13×C23)

Splittings

Fitting, socle, HallC5×C11×C13×C23 ⋊ C2
derived, HallC5×C11 ⋊ C2×C13×C23
HallC11×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ D11
HallC5×C11×C23 ⋊ C2×C13
HallC5×C11×C13 ⋊ C2×C23
HallC11×C23 ⋊ D5×C13
HallC11×C13 ⋊ D5×C23
HallC5×C23 ⋊ C13×D11
HallC5×C13 ⋊ D11×C23
SylowC11 ⋊ D5×C13×C23
SylowC5 ⋊ C13×D11×C23

Subgroups

subgroupG/H
center, hypercenterC13×C23D55
commutator, cosocle, hypocenterC5×C11C2×C13×C23
FrattiniC1G
Fitting, socleC5×C11×C13×C23C2
LCSG ▷ C5×C11
UCSC1 ◁ C13×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16445

Conjugacy classes & character table

8671 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 15);