Finite Group Databasebeta

C2×#14529243 #17036112

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14529243

Splittings

SylowC17 ⋊ C2×#1899

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC22×C17×#123C2
socleC23×C17C2×C22⋊C4
prime radicalC23×D4×C17C22
cosocleC24×C17C24
hypercenterC22×#123D17
hypocenterC17C2×#1899
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#123

2066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171356);