Finite Group Databasebeta

C2×#14530849 #17188583

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14530849

Splittings

FittingC2×C17×#358 ⋊ C2
SylowC17 ⋊ C2×#2211

Subgroups

subgroupG/H
centerC23D8×D17
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC2×C17×#358C2
socleC23×C17C2×D8
prime radicalC22×D136C22
hypercenterC2×#358D17
hypocenterC17C2×#2211
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323827);