Finite Group Databasebeta

C8×C22⋊C4×D17 #17031890

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC8×C22⋊C4×D17

Splittings

FittingC8×C22⋊C4×C17 ⋊ C2
SylowC17 ⋊ C2×C8×C22⋊C4

Subgroups

subgroupG/H
centerC22×C8C22×D17
commutatorC2×C17C22×C4×C8
FrattiniC22×C4C23×D17
FittingC8×C22⋊C4×C17C2
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenterC8×C22⋊C4D17
hypocenterC17C2×C8×C22⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C8×C22⋊C4

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167134);