Finite Group Databasebeta

C2×#14540236 #17907279

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14540236

Splittings

FittingC2×C17×#462 ⋊ C2
SylowC17 ⋊ C2×#3261

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#462C2
socleC23×C17C22×D4
prime radicalC23×D17C2×D4
hypercenterC2×#462D17
hypocenterC17C2×#3261
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

1754 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1042523);