Finite Group Databasebeta

C2×C4×#10587532 #17968124

order4352
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×C4×#10587532

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC2×C42C2×#595
commutatorC2×C17C2×C43
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC23×C17C2×C42
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
hypercenterC2×C4×C8#595
hypocenterC17C2×C4×#97
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

1790 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, 1103368);