Finite Group Databasebeta

D4×#67267 #15682134

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#67267

Splittings

SylowC23 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D23
commutator, socleC22×C23C23×C4
FittingC2×C4×D4×C23C2
prime radicalC22×D4×C23C4
cosocleC2×C4×C23C24
hypercenterC2×C4×D4D23
hypocenterC23D4×M16
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13247);