Finite Group Databasebeta

C2×#14530569 #17187355

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14530569

Splittings

FittingC2×C17×#366 ⋊ C2
SylowC17 ⋊ C2×#2159

Subgroups

subgroupG/H
centerC23D8×D17
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC2×C17×#366C2
socleC23×C17C2×D8
prime radicalC23×D17D8
cosocleC2×C8×C17C24
hypercenterC2×#366D17
hypocenterC17C2×#2159
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322599);