Finite Group Databasebeta

C2×#30656567 #45666112

order32896
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#30656567

Splittings

SylowC257 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D2056
commutatorC8×C257C22×C4
FrattiniC2×C8C22×D257
FittingC22×C16×C257C2
socleC22×C257#107
prime radicalC23×C257Q16
cosocleC2×C8×C257C23
hypercenterC22×C16D257
hypocenterC257C2×#368
LCSG ▷ C8×C257 ▷ C4×C257 ▷ C2×C257 ▷ C257
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16448

Conjugacy classes & character table

8236 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 6302);