Finite Group Databasebeta

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C13×D23×C11⋊C5 #45659783

order32890
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D23×C11⋊C5
unambiguous semidirect productC23⋊(C2×C13×C11⋊C5)
unambiguous semidirect product(C11×D23)⋊(C5×C13)
unambiguous semidirect product(C11×C13×D23)⋊C5

Splittings

Fitting, socle, HallC11×C13×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C2×C5×C13
HallC13×C23×C11⋊C5 ⋊ C2
HallC11×C13×D23 ⋊ C5
HallC23×C11⋊C5 ⋊ C2×C13
HallC11×D23 ⋊ C5×C13
HallC13×C23 ⋊ C2×C11⋊C5
HallC11×C13 ⋊ C5×D23
SylowC23 ⋊ C2×C13×C11⋊C5
SylowC11 ⋊ C5×C13×D23

Subgroups

subgroupG/H
center, hypercenterC13D23×C11⋊C5
commutator, cosocle, hypocenterC11×C23C2×C5×C13
FrattiniC1G
Fitting, socleC11×C13×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3289

Conjugacy classes & character table

1183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 26);