Finite Group Databasebeta

C2×#14530996 #17189206

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

Aliases

direct productC2×#14530996

Splittings

SylowC17 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC22#11763125
commutator, cosocleC2×C8×C17C24
FrattiniC2×C8C23×D17
Fitting, prime radicalC2×C17×#469C2
socleC22×C17#481
hypercenterC2×#469D17
hypocenterC17C2×#2238
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#469

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 324450);