Finite Group Databasebeta

C2×#14544833 #17970105

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14544833

Splittings

FittingC2×C17×#120 ⋊ C4
SylowC17 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#11763757
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC2×C17×#120C4
socleC22×C17#386
prime radicalC2×#11763369C2
cosocleC23×D17C24
hypercenterC2×#120#595
hypocenterC17C2×#1913
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C2×#120

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105349);