Finite Group Databasebeta

C4×#11762546 #16925203

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11762546

Splittings

SylowC17 ⋊ C4×#328

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC2×C4×C17C2×C42
FrattiniC23×C4C22×D17
FittingC4×C17×C22⋊Q8C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC4×C22⋊Q8D17
hypocenterC17C4×#328
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60447);