Finite Group Databasebeta

Q8×#6435 #13513220

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productQ8×#6435

Splittings

FittingC42×C7×Q8 ⋊ C2
SylowC7 ⋊ Q8×#117

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC42×C7×Q8C2
socle, cosocleC23×C7C25
prime radicalC23×D7C24
hypercenterC42×Q8D7
hypocenterC7Q8×#117
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C42×Q8

2434 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, 328992);