Finite Group Databasebeta

C4×#11719148 #16796985

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11719148

Splittings

SylowC13 ⋊ C4×#413

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC22×#6129C22
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13C4×#413
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

1570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103634);