Finite Group Databasebeta

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D5×C13×C23⋊C11 #45659779

order32890
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productD5×C13×C23⋊C11
unambiguous semidirect productC5⋊(C2×C13×C23⋊C11)
unambiguous semidirect product(D5×C23)⋊(C11×C13)
unambiguous semidirect product(D5×C13×C23)⋊C11

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C2×C11×C13
HallC5×C13×C23⋊C11 ⋊ C2
HallD5×C13×C23 ⋊ C11
HallC5×C23⋊C11 ⋊ C2×C13
HallC13×C23 ⋊ D5×C11
HallD5×C23 ⋊ C11×C13
HallC5×C13 ⋊ C2×C23⋊C11
SylowC23 ⋊ D5×C11×C13
SylowC5 ⋊ C2×C13×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC13D5×C23⋊C11
commutator, cosocle, hypocenterC5×C23C2×C11×C13
FrattiniC1G
Fitting, socleC5×C13×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1495

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 22);