Finite Group Databasebeta

C8×#10587494 #16924883

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

Aliases

direct productC8×#10587494

Splittings

FittingC8×M16×C17 ⋊ C2
SylowC17 ⋊ C8×#100

Subgroups

subgroupG/H
centerC2×C8#63227
commutatorC22×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC8×M16×C17C2
socleC22×C17C4×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C42×C17C23
hypercenterC8×M16D17
hypocenterC17C8×#100
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×M16

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 60127);