Finite Group Databasebeta

C4×#11763705 #17960704

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11763705

Splittings

SylowC17 ⋊ C4×#349

Subgroups

subgroupG/H
centerC42C22⋊#595
commutatorC22×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC22×C42×C17C4
socleC22×C17C2×C22⋊C8
prime radicalC24×C17C2×C8
cosocleC22×#3622C23
hypercenterC22×C42#595
hypocenterC17C4×#349
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C42 ◁ C22×C42

522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095948);