Finite Group Databasebeta

M16×C4⋊#261 #16797154

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productM16×C4⋊#261

Splittings

FittingC4×C13×M16 ⋊ C4
SylowC13 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC4×C13×M16C4
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC4×M16#261
hypocenterC13C4⋊C4×M16
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16

1242 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, 1103803);