Finite Group Databasebeta

C22×#90327 #14260766

order1792
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#90327

Splittings

FittingC22×C7×C22⋊Q8 ⋊ C2
SylowC7 ⋊ C22×#554

Subgroups

subgroupG/H
centerC24C23×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC22×C7×C22⋊Q8C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22×C22⋊Q8D7
hypocenterC7C22×#554
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

8454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076538);