Finite Group Databasebeta

C2×D9×C4⋊C8 #11858209

order1152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D9×C4⋊C8

Splittings

FittingC2×C9×C4⋊C8 ⋊ C2
SylowC9 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D9
commutatorC2×C9C23×C8
FrattiniC2×C3×C4C23×D3
FittingC2×C9×C4⋊C8C2
socleC23×C3C2×C4×D3
prime radicalC23×D9C2×C4
cosocleC2×C4×C9C24
hypercenterC2×C4⋊C8D9
hypocenterC9C22×C4⋊C8
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 92220);