Finite Group Databasebeta

D4×#88237 #16807584

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productD4×#88237

Splittings

FittingC2×C4×D4×C13 ⋊ C4
SylowC13 ⋊ D4×#117

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C4×D4×C13C4
prime radicalC22×D4×D13C22
cosocleC22×D13C25
hypercenterC2×C4×D4#261
hypocenterC13D4×#117
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1114233);