Finite Group Databasebeta

C4×#11718155 #15778172

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

Aliases

direct productC4×#11718155

Splittings

SylowC13 ⋊ C4×#361

Subgroups

subgroupG/H
centerC2×C4#88072
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC2×C4×C13×D8C2
socleC22×C13C2×#102
prime radicalC22×C13×D8C22
cosocleC22×C8×C13C23
hypercenterC2×C4×D8D13
hypocenterC13C4×#361
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 84821);