Finite Group Databasebeta

← Prev (#13085217) Next (#13085219) →

C2×D5×Q8⋊C9 #13085218

order1440
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×Q8⋊C9
unambiguous semidirect productC5⋊(C22×Q8⋊C9)
unambiguous semidirect product(C2×C5)⋊(C2×Q8⋊C9)
unambiguous semidirect product(C2×Q8×D5)⋊C9

Splittings

derivedC5×Q8 ⋊ C22×C9
HallC2×Q8×D5 ⋊ C9
SylowC5 ⋊ C22×Q8⋊C9

Subgroups

subgroupG/H
center, hypercenterC22×C3D5×A4
commutator, hypocenterC5×Q8C22×C9
FrattiniC2×C3C2×D5×A4
FittingC2×C3×C5×Q8C2×C3
socleC22×C3×C5C2×A4
prime radicalC22×C3×D5A4
cosocleC3×C5×Q8C22×C3
LCSG ▷ C5×Q8
UCSC1 ◁ C22×C3

202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 720

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1535);