Finite Group Databasebeta

D4×#88072 #15878325

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×#88072

Splittings

SylowC13 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×D42×C13C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×D42D13
hypocenterC13D4×#102
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 184974);