Finite Group Databasebeta

D4×#16813868 #44408471

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD4×#16813868

Splittings

SylowC227 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D227
commutator, socleC22×C227C23×C4
FittingC2×C4×D4×C227C2
prime radicalC22×D4×C227C4
cosocleC2×C4×C227C24
hypercenterC2×C4×D4D227
hypocenterC227D4×M16
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

4570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13247);