Finite Group Databasebeta

C8×#10587534 #17952346

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

Aliases

direct productC8×#10587534

Splittings

FittingC82×C17 ⋊ C4
SylowC17 ⋊ C8×#107

Subgroups

subgroupG/H
centerC2×C8C4⋊#595
commutatorC4×C17C2×C4×C8
FrattiniC42C22×#595
FittingC82×C17C4
socleC22×C17C4×C4⋊C4
prime radicalC22×D17C4×D4
cosocleC42×D17C23
hypercenterC82#595
hypocenterC17C8×#107
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C82

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1087590);