Finite Group Databasebeta

C22×#89761 #13512100

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#89761

Splittings

FittingC23×C7×C4⋊C4 ⋊ C2
SylowC7 ⋊ C22×#385

Subgroups

subgroupG/H
centerC25C22×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC23×C7×C4⋊C4C2
socleC25×C7C23
prime radicalC25×D7C22
cosocleC23×C7C25
hypercenterC23×C4⋊C4D7
hypocenterC7C22×#385
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C25 ◁ C23×C4⋊C4

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 327872);