Finite Group Databasebeta

C4×#89500 #13352148

order1792
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#89500

Splittings

FittingC4×C7×C22⋊C8 ⋊ C2
SylowC7 ⋊ C4×#435

Subgroups

subgroupG/H
centerC2×C42C22×D7
commutatorC22×C7C22×C42
FrattiniC22×C4C23×D7
FittingC4×C7×C22⋊C8C2
socleC23×C7C23×C4
prime radicalC22×C22⋊D7C2×C4
cosocleC22×C4×C7C24
hypercenterC4×C22⋊C8D7
hypocenterC7C4×#435
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

1282 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, 167920);