Finite Group Databasebeta

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C22×#11719138 #16808095

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#11719138
unambiguous semidirect productD13⋊(C2×#418)

Splittings

FittingC23×D4×C13 ⋊ C4
SylowC13 ⋊ C22×#418

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC23×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D4×D13C2
cosocleC4×D13C25
hypercenterC23×D4#261
hypocenterC13C22×#418
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1114744);