Finite Group Databasebeta

C8×#10587507 #16924887

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

Aliases

direct productC8×#10587507

Splittings

SylowC17 ⋊ C8×#101

Subgroups

subgroupG/H
centerC2×C8C22⋊Dic17
commutatorC22×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC2×C8×Q8×C17C2
socleC22×C17C4×C22⋊C4
prime radicalC23×C17C2×C42
cosocleC2×C42×C17C23
hypercenterC2×C8×Q8D17
hypocenterC17C8×#101
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60131);