Finite Group Databasebeta

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D5×C11×C13×C23 #45659768

order32890
automorphism?
homologyAbelianization (H1) = C2×C11×C13×C23 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC5×C11×C13×C23 ⋊ C2
derived, SylowC5 ⋊ C2×C11×C13×C23
HallC5×C13×C23 ⋊ C2×C11
HallC5×C11×C23 ⋊ C2×C13
HallC5×C11×C13 ⋊ C2×C23
HallC5×C23 ⋊ C2×C11×C13
HallC5×C13 ⋊ C2×C11×C23
HallC5×C11 ⋊ C2×C13×C23

Subgroups

subgroupG/H
center, hypercenterC11×C13×C23D5
commutator, cosocle, hypocenterC5C2×C11×C13×C23
FrattiniC1G
Fitting, socleC5×C11×C13×C23C2
LCSG ▷ C5
UCSC1 ◁ C11×C13×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16445

Conjugacy classes & character table

13156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 11);