Finite Group Databasebeta

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C22⋊C4×C22⋊#261 #16791610

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×C22⋊#261

Splittings

FittingC22×C13×C22⋊C4 ⋊ C4
SylowC13 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC22×C13×C22⋊C4C4
socleC23×C13C23×C4
prime radicalC25×D13C22
cosocleC23×D13C24
hypercenterC22×C22⋊C4#261
hypocenterC13C22⋊C42
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1098259);