Finite Group Databasebeta

Q8×#88064 #15879491

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

Aliases

direct productQ8×#88064

Splittings

SylowC13 ⋊ Q8×#101

Subgroups

subgroupG/H
centerC22C22×#6103
commutator, prime radicalC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingQ8×C13×M16C2
socleC22×C13C22×C22⋊C4
cosocleC22×C4×C13C24
hypercenterQ8×M16D13
hypocenterC13Q8×#101
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 186140);