Finite Group Databasebeta

C2×#22572065 #31732204

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22572065

Splittings

FittingC2×#465×C67 ⋊ C2
SylowC67 ⋊ C2×#3297

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#465×C67C2
socleC23×C67C22×D4
hypercenterC2×#465D67
hypocenterC67C2×#3297
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

2350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1522 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1045941);