Finite Group Databasebeta

C2×#30681221 #46777693

order33632
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30681221

Splittings

SylowC1051 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D1051
commutator, cosocleC4×C1051C23
FrattiniC4C22×D1051
Fitting, prime radicalC2×D4×C1051C2
socleC22×C1051D4
hypercenterC2×D4D1051
hypocenterC1051C2×SD16
LCSG ▷ C4×C1051 ▷ C2×C1051 ▷ C1051
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16816

Conjugacy classes & character table

5264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33632, 160);