Finite Group Databasebeta

D4×D13⋊M16 #16808288

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×D13⋊M16
unambiguous semidirect productD13⋊(D4×M16)

Splittings

SylowC13 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC2×C4×D4×C13C4
prime radicalC22×D4×D13C4
cosocleC2×Dic13C25
hypercenterC2×C4×D4#261
hypocenterC13C2×D4×M16
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114937);