Finite Group Databasebeta

D4×#88063 #15878265

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#88063

Splittings

FittingD4×C13×M16 ⋊ C2
SylowC13 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×M16C2
socleC22×C13C22×C22⋊C4
prime radicalC2×D4×D52C2
cosocleC22×C4×C13C24
hypercenterD4×M16D13
hypocenterC13D4×#100
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 184914);