Finite Group Databasebeta

Q8×C4⋊C4×D13 #16022217

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

Aliases

direct productQ8×C4⋊C4×D13

Splittings

FittingQ8×C13×C4⋊C4 ⋊ C2
SylowC13 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingQ8×C13×C4⋊C4C2
socle, cosocleC23×C13C25
prime radicalC23×D13C24
hypercenterQ8×C4⋊C4D13
hypocenterC13C2×Q8×C4⋊C4
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 328866);