Finite Group Databasebeta

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C22⋊C4×#6122 #16796945

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

Aliases

direct productC22⋊C4×#6122

Splittings

SylowC13 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC22×C13×C22⋊C4C4
socleC23×C13C23×C4
prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C22⋊C4×M16
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C22⋊C4

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103594);