Finite Group Databasebeta

C2×#14545037 #17978216

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545037

Splittings

FittingC2×C17×#117 ⋊ C4
SylowC17 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC2×C4#10587539
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC2×#11763321C2
cosocleC2×C22⋊D17C24
hypercenterC2×#117#595
hypocenterC17C2×#2120
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

1398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113460);