Finite Group Databasebeta

C2×#14544852 #17970169

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

Aliases

direct productC2×#14544852

Splittings

FittingC2×C17×#107 ⋊ C4
SylowC17 ⋊ C2×#1922

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#107C4
socleC23×C17C4×D4
prime radicalC23×D17#41
cosocleC2×C4×D17C24
hypercenterC2×#107#595
hypocenterC17C2×#1922
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105413);