Finite Group Databasebeta

C22×D4⋊#1057 #16793279

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×D4⋊#1057

Splittings

SylowC13 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC24C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
Fitting, prime radicalC23×D4×C13C4
socleC24×C13C22⋊C4
cosocleC4×Dic13C24
hypercenterC23×D4#261
hypocenterC13C22×D4⋊C8
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D4

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1099928);