Finite Group Databasebeta

C2×C8×D4×D17 #17898152

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC2×C8×D4×D17

Splittings

FittingC2×C8×D4×C17 ⋊ C2
SylowC17 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC22×C8C22×D17
commutatorC2×C17C24×C8
FrattiniC2×C4C24×D17
FittingC2×C8×D4×C17C2
socleC23×C17C23×C4
prime radicalC22×D4×D17C4
cosocleC2×C4×C17C25
hypercenterC2×C8×D4D17
hypocenterC17C22×C8×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

3694 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, 1033396);