Finite Group Databasebeta

C8×(C2×#595)⋊C4 #17956587

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×(C2×#595)⋊C4

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C8×#95

Subgroups

subgroupG/H
centerC22×C8C2×#595
commutatorC2×C17C42×C8
FrattiniC22×C4C22×#595
FittingC2×C4×C8×C17C4
socleC23×C17C2×C42
prime radicalC23×D17C22×C4
cosocleC22×C4×D17C23
hypercenterC2×C4×C8#595
hypocenterC17C8×#95
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1174 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, 1091831);