Finite Group Databasebeta

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C22×C4⋊C4×Dic13 #16021099

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4⋊C4×Dic13

Splittings

SylowC13 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC25C22×D13
commutatorC2×C13C23×C42
FrattiniC23C24×D13
FittingC23×C13×C4⋊C4C2
socle, prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC23×C4⋊C4D13
hypocenterC13C22×C4×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C23×C4⋊C4

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327748);