Finite Group Databasebeta

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C22×#72209832 #72275445

order12288
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C210

Aliases

direct productC22×#72209832

Splittings

FittingC22×#6499874 ⋊ D3
derived#11710730 ⋊ C24

Subgroups

subgroupG/H
center, socleC23#72209653
commutator, cosocle, hypocenter#11710730C24
FrattiniC24C23×#1020
FittingC22×#6499874D3
hypercenterC24#87588⋊C2
LCSG ▷ #11710730
UCSC1 ◁ C23 ◁ C24

Only the 235 normal subgroups are shown; non-normal subgroups are omitted.

normal subgroups only

Only the group's 235 normal subgroups are shown; non-normal subgroups are omitted.

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

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

automorphism group ofC22×C3×M16

GAP

Past the SmallGroups library coverage — no SmallGroups id.