Finite Group Databasebeta

← Prev (#17968448) Next (#17968450) →

C4×#11763802 #17968449

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11763802

Splittings

FittingC2×C4×Q8×C17 ⋊ C4
SylowC17 ⋊ C4×#419

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC23×D17C2×D4
cosocleC2×C4×D17C24
hypercenterC2×C4×Q8#595
hypocenterC17C4×#419
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

1586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103693);