Finite Group Databasebeta

C2×#14530858 #17188702

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

Aliases

direct productC2×#14530858

Splittings

FittingC2×C17×#509 ⋊ C2
SylowC17 ⋊ C2×#2213

Subgroups

subgroupG/H
centerC22#11763002
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
FittingC2×C17×#509C2
socleC22×C17#459
hypercenterC2×#509D17
hypocenterC17C2×#2213
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 323946);