Finite Group Databasebeta

C2×(C2×D1039)⋊C4 #45685158

order33248
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×(C2×D1039)⋊C4

Splittings

FittingC22×C4×C1039 ⋊ C2
SylowC1039 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1039
commutatorC2×C1039C22×C4
FrattiniC22C22×D1039
FittingC22×C4×C1039C2
socleC23×C1039C22
prime radicalC23×D1039C2
cosocleC22×C1039C23
hypercenterC22×C4D1039
hypocenterC1039C2×C22⋊C4
LCSG ▷ C2×C1039 ▷ C1039
UCSC1 ◁ C23 ◁ C22×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16624

Conjugacy classes & character table

8324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33248, 97);