Finite Group Databasebeta

C2×#14530837 #17188558

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

Aliases

direct productC2×#14530837

Splittings

SylowC17 ⋊ C2×#2210

Subgroups

subgroupG/H
centerC23D8×D17
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
Fitting, prime radicalC22×C17×D16C2
socleC23×C17C2×D8
hypercenterC22×D16D17
hypocenterC17C2×#2210
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323802);