Finite Group Databasebeta

C2×#14530036 #17062085

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14530036

Splittings

FittingC2×C17×#342 ⋊ C2
SylowC17 ⋊ C2×#2044

Subgroups

subgroupG/H
centerC23#10587568
commutator, cosocleC24×C17C24
FrattiniC24C23×D17
FittingC2×C17×#342C2
socleC23×C17#120
prime radicalC2×#11763371C2
hypercenterC2×#342D17
hypocenterC17C2×#2044
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 197329);