Finite Group Databasebeta

C2×#14544617 #17969176

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

Aliases

direct productC2×#14544617

Splittings

SylowC17 ⋊ C2×#1783

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC23×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D4×D17C2
cosocleC22×Dic17C24
hypercenterC23×D4#595
hypocenterC17C2×#1783
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

5942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104420);