Finite Group Databasebeta

C8×#6470 #13319385

order1792
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#6470

Splittings

FittingC7×C8×M16 ⋊ C2
SylowC7 ⋊ C8×#131

Subgroups

subgroupG/H
centerC4×C8C22×D7
commutatorC2×C7C22×C4×C8
FrattiniC42C23×D7
FittingC7×C8×M16C2
socleC22×C7C22×C42
prime radicalC2×#1157C2×C4
cosocleC42×C7C24
hypercenterC8×M16D7
hypocenterC7C8×#131
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C4×C8 ◁ C8×M16

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 135157);