Finite Group Databasebeta

C4×C22⋊#6092 #16789284

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

Aliases

direct productC4×C22⋊#6092

Splittings

SylowC13 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
centerC2×C42C2×#261
commutatorC2×C13C2×C4×C16
FrattiniC22×C4C22×#261
FittingC22×C42×C13C4
socleC23×C13C22×C8
prime radicalC24×C13C2×C8
cosocleC22×#1055C23
hypercenterC22×C42#261
hypocenterC13C4×C22⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C22×C42

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1095933);