Finite Group Databasebeta

C4×D4×#1057 #16797336

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D4×#1057

Splittings

SylowC13 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic13C24
hypercenterC2×C4×D4#261
hypocenterC13C4×C8×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103985);