Finite Group Databasebeta

D4×#88059 #15881172

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#88059

Splittings

SylowC13 ⋊ D4×#108

Subgroups

subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C8×D4×C13C2
socleC22×C13C22×C4⋊C4
prime radicalC22×D4×C13Q8
cosocleC22×C4×C13C24
hypercenterC2×C8×D4D13
hypocenterC13D4×#108
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C2×C8×D4

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 187821);