Finite Group Databasebeta

C2×#14530078 #17062193

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530078

Splittings

FittingC22×C17×#108 ⋊ C2
SylowC17 ⋊ C2×#2051

Subgroups

subgroupG/H
centerC23#10587581
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#108C2
socleC23×C17#121
prime radicalC22×#10587594C2
hypercenterC22×#108D17
hypocenterC17C2×#2051
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

1490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 197437);