Finite Group Databasebeta

C32×D7×C22⋊C4 #72246721

order2016
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productC32×D7×C22⋊C4

Splittings

FittingC32×C7×C22⋊C4 ⋊ C2
HallC32×C7 ⋊ C2×C22⋊C4
SylowC7 ⋊ C2×C32×C22⋊C4

Subgroups

subgroupG/H
centerC22×C32C22×D7
commutatorC2×C7C22×C32×C4
FrattiniC22C22×C32×D7
FittingC32×C7×C22⋊C4C2
socleC22×C32×C7C23
prime radicalC23×C32×D7C2
cosocleC22×C7C23×C32
hypercenterC32×C22⋊C4D7
hypocenterC7C2×C32×C22⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C32 ◁ C32×C22⋊C4

792 conjugacy classes of subgroups; only the 294 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 294 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) = 504

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD7×C22⋊C4×C3⋊D3, C32×D7×#120, D7×#64091, …
maximal normal subgroup ofD7×C22⋊C4×C3⋊D3, C32×D7×#120, D7×#64091, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.