Finite Group Databasebeta

C2×#14530157 #17062907

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530157

Splittings

FittingC22×C17×C4⋊C8 ⋊ C2
SylowC17 ⋊ C2×#2065

Subgroups

subgroupG/H
centerC24C2×D68
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×C4⋊C8C2
socleC24×C17C2×D4
prime radicalC23×D68C22
hypercenterC22×C4⋊C8D17
hypocenterC17C2×#2065
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 198151);