Finite Group Databasebeta

C2×#14528826 #17033943

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

Aliases

direct productC2×#14528826

Splittings

SylowC17 ⋊ C2×#1811

Subgroups

subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC23×M16×C17C2
socleC23×C17C2×C4⋊C4
prime radicalC25×C17Q8
cosocleC22×C4×C17C24
hypercenterC23×M16D17
hypocenterC17C2×#1811
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×M16

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 169187);