Finite Group Databasebeta

Q8×#88056 #15879527

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#88056

Splittings

SylowC13 ⋊ Q8×#103

Subgroups

subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C8×Q8×C13C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×C8×Q8D13
hypocenterC13Q8×#103
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 186176);