Finite Group Databasebeta

C2×#97×#595 #17968123

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

Aliases

direct productC2×#97×#595

Splittings

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

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C2×C43
FrattiniC2×C4C23×#595
FittingC2×C17×#97C4
socleC23×C17C2×C42
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
hypercenterC2×#97#595
hypocenterC17C2×C4×#97
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#97

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103367);