Finite Group Databasebeta

C2×C4×#10587593 #17897729

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#10587593

Splittings

FittingC2×C4×M16×C17 ⋊ C2
SylowC17 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC2×C17C23×C42
FrattiniC2×C4C24×D17
FittingC2×C4×M16×C17C2
socleC23×C17C23×C4
prime radicalC22×#63252C22
cosocleC2×C4×C17C25
hypercenterC2×C4×M16D17
hypocenterC17C2×C4×#131
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1032973);