Finite Group Databasebeta

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C5×C11×C23×D13 #45659762

order32890
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C23×D13
unambiguous semidirect productC13⋊(C2×C5×C11×C23)

Splittings

Fitting, socle, HallC5×C11×C13×C23 ⋊ C2
derived, SylowC13 ⋊ C2×C5×C11×C23
HallC11×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ C2×C11
HallC5×C11×C13 ⋊ C2×C23
HallC13×C23 ⋊ C2×C5×C11
HallC11×C13 ⋊ C2×C5×C23
HallC5×C13 ⋊ C2×C11×C23

Subgroups

subgroupG/H
center, hypercenterC5×C11×C23D13
commutator, cosocle, hypocenterC13C2×C5×C11×C23
FrattiniC1G
Fitting, socleC5×C11×C13×C23C2
LCSG ▷ C13
UCSC1 ◁ C5×C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16445

Conjugacy classes & character table

10120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 5);