Finite Group Databasebeta

C4×#11718131 #15778056

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11718131

Splittings

SylowC13 ⋊ C4×#352

Subgroups

subgroupG/H
centerC2×C4#88074
commutatorC23×C13C2×C42
FrattiniC22×D4C22×D13
FittingC4×C13×#123C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#123D13
hypocenterC13C4×#352
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84705);