Finite Group Databasebeta

Q8×(C2×D7)⋊C8 #13370309

order1792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×(C2×D7)⋊C8

Splittings

FittingC2×C7×C8×Q8 ⋊ C2
SylowC7 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D7
commutatorC22×C7C23×C8
FittingC2×C7×C8×Q8C2
socleC23×C7C23×C4
prime radicalC23×D7C22×C4
cosocleC22×C4×C7C24
hypercenterC2×C8×Q8D7
hypocenterC7Q8×C22⋊C8
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 186081);