Finite Group Databasebeta

C8×#10587486 #16923674

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

Aliases

direct productC8×#10587486

Splittings

SylowC17 ⋊ C8×#97

Subgroups

subgroupG/H
centerC2×C4×C8C2×D17
commutatorC2×C17C42×C8
FrattiniC2×C42C22×D17
FittingC2×C82×C17C2
socle, prime radicalC23×C17C2×C42
cosocleC2×C42×C17C23
hypercenterC2×C82D17
hypocenterC17C8×#97
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 58918);