Finite Group Databasebeta

C2×#30658310 #45683140

order33056
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30658310

Splittings

FittingC2×D4×C1033 ⋊ C2
SylowC1033 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22C22⋊D1033
commutator, cosocleC4×C1033C23
FrattiniC4C22×D1033
FittingC2×D4×C1033C2
socleC22×C1033D4
hypercenterC2×D4D1033
hypocenterC1033C2×D8
LCSG ▷ C4×C1033 ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16528

Conjugacy classes & character table

5174 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 156);