Finite Group Databasebeta

Q8×#6464 #14218207

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#6464

Splittings

FittingC2×C7×C8×Q8 ⋊ C2
SylowC7 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D7
commutator, socleC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×C8×Q8C2
prime radicalC2×#1157C23
cosocleC2×C4×C7C25
hypercenterC2×C8×Q8D7
hypocenterC7Q8×#131
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C8 ◁ C2×C8×Q8

1882 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, 1033979);