Finite Group Databasebeta

D4×Q8×#261 #16807623

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×Q8×#261

Splittings

FittingD4×Q8×C13 ⋊ C4
SylowC13 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingD4×Q8×C13C4
prime radicalC2×D4×D13C23
cosocleC22×D13C25
hypercenterD4×Q8#261
hypocenterC13C4×D4×Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ D4×Q8

3148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114272);