Finite Group Databasebeta

C8×#6461 #13362011

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productC8×#6461

Splittings

FittingC7×C8×C4⋊C4 ⋊ C2
SylowC7 ⋊ C8×#126

Subgroups

subgroupG/H
centerC22×C8C22×D7
commutatorC22×C7C23×C8
FrattiniC22×C4C23×D7
FittingC7×C8×C4⋊C4C2
socleC23×C7C23×C4
prime radicalC23×D7C22×C4
cosocleC22×C4×C7C24
hypercenterC8×C4⋊C4D7
hypocenterC7C8×#126
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

786 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, 177783);