Finite Group Databasebeta

C22⋊C4×D1063 #46801145

order34016
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D1063

Splittings

FittingC22⋊C4×C1063 ⋊ C2
SylowC1063 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1063
commutatorC2×C1063C22×C4
FittingC22⋊C4×C1063C2
socle, cosocleC22×C1063C23
prime radicalC23×D1063C2
hypercenterC22⋊C4D1063
hypocenterC1063C2×C22⋊C4
LCSG ▷ C2×C1063 ▷ C1063
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8504

Conjugacy classes & character table

5330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34016, 96);