Finite Group Databasebeta

C2×#14537243 #17897792

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14537243

Splittings

FittingC2×C17×#410 ⋊ C2
SylowC17 ⋊ C2×#2883

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#410C2
socleC22×C17C22×C22⋊C4
prime radicalC22×#10587696C2
cosocleC23×C17C25
hypercenterC2×#410D17
hypocenterC17C2×#2883
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

5338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033036);