Finite Group Databasebeta

C2×#14537248 #17897798

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14537248

Splittings

SylowC17 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
Fitting, prime radicalC22×C17×2−1+4C2
socleC22×C17C22×C22⋊C4
cosocleC23×C17C25
hypercenterC22×2−1+4D17
hypocenterC17C2×#2884
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C22×2−1+4

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033042);