Finite Group Databasebeta

C22⋊C4×#6092 #16789347

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×#6092

Splittings

SylowC13 ⋊ C16×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×#261
commutatorC2×C13C2×C4×C16
FittingC4×C13×C22⋊C4C4
socleC23×C13C22×C8
prime radicalC24×C13C2×C8
cosocleC22×#1055C23
hypercenterC4×C22⋊C4#261
hypocenterC13C16×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1095996);