Finite Group Databasebeta

C22×M16×#261 #16807999

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×M16×#261

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C23×C42
FrattiniC4C24×#261
FittingC22×C13×M16C4
socleC23×C13C2×C42
prime radicalC24×D13C2×C4
cosocleC4×D13C25
hypercenterC22×M16#261
hypocenterC13C22×C4×M16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×M16

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114648);