Finite Group Databasebeta

C2×#14530892 #17188776

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14530892

Splittings

SylowC17 ⋊ C2×#2219

Subgroups

subgroupG/H
centerC23C2×D136
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC22×C17×M32C2
socleC23×C17C2×D8
prime radicalC24×C17D8
hypercenterC22×M32D17
hypocenterC17C2×#2219
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 324020);