Finite Group Databasebeta

Q8×#88100 #16797476

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#88100

Splittings

FittingC8×Q8×C13 ⋊ C4
SylowC13 ⋊ Q8×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC8×Q8×C13C4
prime radicalC22×D13C23×C4
cosocleC2×C4×D13C24
hypercenterC8×Q8#261
hypocenterC13Q8×#97
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C8×Q8

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1104125);