Finite Group Databasebeta

C4×#90326 #13513768

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#90326

Splittings

FittingC4×C7×C22⋊Q8 ⋊ C2
SylowC7 ⋊ C4×#554

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC4×C7×C22⋊Q8C2
socle, cosocleC23×C7C25
prime radicalC22×C22⋊D7C23
hypercenterC4×C22⋊Q8D7
hypocenterC7C4×#554
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

2516 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, 329540);