Finite Group Databasebeta

C2×C4×#10587504 #17031990

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#10587504

Splittings

SylowC17 ⋊ C2×C4×#100

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC22×C17C22×C42
FrattiniC22×C4C23×D17
FittingC22×C4×D4×C17C2
socleC23×C17C2×C22⋊C4
prime radicalC23×D4×C17C22
cosocleC22×C4×C17C24
hypercenterC22×C4×D4D17
hypocenterC17C2×C4×#100
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×D4

1970 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, 167234);