Finite Group Databasebeta

C2×D8×C9⋊D9 #72244138

order5184
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26×C9

Aliases

direct productC2×D8×C9⋊D9

Splittings

FittingC2×C92×D8 ⋊ C2
SylowC92 ⋊ C22×D8

Subgroups

subgroupG/H
centerC22D4×C9⋊D9
commutator, cosocleC4×C92C24
FrattiniC32×C4C23×C3⋊D3
FittingC2×C92×D8C2
socleC22×C32D4×C3⋊D3
hypercenterC2×D8C9⋊D9
hypocenterC92C22×D8
LCSG ▷ C4×C92 ▷ C2×C92 ▷ C92
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

3887 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1296

Conjugacy classes & character table

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

Relationships

maximal subgroup of#442×C9⋊D9, C2×D8×#92314, C2×AGL(1,ℤ/8)×C9⋊D9
maximal normal subgroup of#442×C9⋊D9, C2×D8×#92314, C2×AGL(1,ℤ/8)×C9⋊D9

GAP

Past the SmallGroups library coverage — no SmallGroups id.