Finite Group Databasebeta

C2×C9⋊(C22⋊(C22⋊C9)) #72276028

order2592
automorphism?
homologyAbelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C24×C3

Aliases

direct productC2×C9⋊(C22⋊(C22⋊C9))

Splittings

SylowC25 ⋊ C9⋊C9

Subgroups

subgroupG/H
centerC2×C32C3×C22⋊A4
commutatorC24×C3C2×C3×C9
FrattiniC32C2×C3×C22⋊A4
FittingC25×C3×C9C3
socle, prime radicalC25×C32C32
cosocleC24×C32C2×C32
hypercenterC2×C3×C9C22⋊A4
hypocenterC24C2×C9⋊C9
LCSG ▷ C24×C3 ▷ C24
UCSC1 ◁ C2×C32 ◁ C2×C3×C9

1438 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 1438 conjugacy classes of subgroups — too many to draw. Only its 148 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) = 324

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×#72229255, C2×C22⋊A4×C9⋊C9, C2×#72229244
maximal normal subgroup ofC2×#72229255, C2×C22⋊A4×C9⋊C9, C2×#72229244

GAP

Past the SmallGroups library coverage — no SmallGroups id.