Finite Group Databasebeta

C8×#6492 #13360755

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#6492

Splittings

FittingC22×C4×C7×C8 ⋊ C2
SylowC7 ⋊ C8×#123

Subgroups

subgroupG/H
centerC22×C8C22×D7
commutatorC22×C7C23×C8
FrattiniC22×C4C23×D7
FittingC22×C4×C7×C8C2
socleC23×C7C23×C4
prime radicalC22×C22⋊D7C2×C4
cosocleC22×C4×C7C24
hypercenterC22×C4×C8D7
hypocenterC7C8×#123
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 176527);