Finite Group Databasebeta

C2×#30658302 #45683081

order33056
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#30658302

Splittings

FittingC22×C4×C1033 ⋊ C2
SylowC1033 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1033
commutatorC2×C1033C22×C4
FrattiniC22C22×D1033
FittingC22×C4×C1033C2
socleC23×C1033C22
prime radicalC23×D1033C2
cosocleC22×C1033C23
hypercenterC22×C4D1033
hypocenterC1033C2×C22⋊C4
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16528

Conjugacy classes & character table

8276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 97);