Finite Group Databasebeta

C4×#11718514 #15861423

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11718514

Splittings

SylowC13 ⋊ C4×#441

Subgroups

subgroupG/H
centerC22×C4D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC4×C13×#106C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC4×#106D13
hypocenterC13C4×#441
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 168072);