Finite Group Databasebeta

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C4×#11719071 #16791538

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#11719071

Splittings

FittingC4×C13×C22⋊C4 ⋊ C4
SylowC13 ⋊ C4×#388

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC4×C13×C22⋊C4C4
socleC23×C13C23×C4
prime radicalC24×D13C23
cosocleC23×D13C24
hypercenterC4×C22⋊C4#261
hypocenterC13C4×#388
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

2134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1098187);