Finite Group Databasebeta

C2×#14528742 #17033613

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14528742

Splittings

FittingC2×C17×#391 ⋊ C2
SylowC17 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC23#10587623
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#391C2
socleC23×C17#120
prime radicalC22×#10587694C2
cosocleC22×C4×C17C24
hypercenterC2×#391D17
hypocenterC17C2×#1793
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#391

3682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 168857);