Finite Group Databasebeta

C4×#89886 #13360277

order1792
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#89886

Splittings

FittingC22×C4×C7×C8 ⋊ C2
SylowC7 ⋊ C4×#465

Subgroups

subgroupG/H
centerC22×C4C2×D28
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC22×C4×C7×C8C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenterC22×C4×C8D7
hypocenterC7C4×#465
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 176049);