Finite Group Databasebeta

C2×#30659016 #45685222

order33248
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30659016

Splittings

FittingC2×C8×C1039 ⋊ C2
SylowC1039 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22D4156
commutator, cosocleC4×C1039C23
FrattiniC4C22×D1039
FittingC2×C8×C1039C2
socleC22×C1039D4
prime radicalC2×D4156C2
hypercenterC2×C8D1039
hypocenterC1039C2×SD16
LCSG ▷ C4×C1039 ▷ C2×C1039 ▷ C1039
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16624

Conjugacy classes & character table

8318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33248, 161);