Finite Group Databasebeta

Q8×#88110 #16797478

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

Aliases

direct productQ8×#88110

Splittings

SylowC13 ⋊ Q8×#97

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC2×C4×Q8×C13C4
socle, prime radicalC23×C13C23×C4
cosocleC22×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13Q8×#97
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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, 1104127);