Finite Group Databasebeta

Q8×#88046 #15879465

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#88046

Splittings

FittingQ8×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ Q8×#99

Subgroups

subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingQ8×C13×C22⋊C4C2
socleC22×C13C22×C22⋊C4
prime radicalC22×C22⋊D13C23
cosocleC24×C13C24
hypercenterQ8×C22⋊C4D13
hypocenterC13Q8×#99
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×Q8 ◁ Q8×C22⋊C4

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 186114);