Finite Group Databasebeta

C8×#10587532 #17950265

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct productC8×#10587532

Splittings

FittingC82×C17 ⋊ C4
SylowC17 ⋊ C8×#97

Subgroups

subgroupG/H
centerC4×C8C2×#595
commutatorC2×C17C42×C8
FrattiniC42C22×#595
FittingC82×C17C4
socleC22×C17C43
prime radicalC22×D17C2×C42
cosocleC42×D17C23
hypercenterC82#595
hypocenterC17C8×#97
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C8 ◁ C82

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1085509);