Finite Group Databasebeta

C2×#14543867 #17960564

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543867

Splittings

FittingC2×C17×#99 ⋊ C4
SylowC17 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC22#11763686
commutatorC23×C17C2×C42
FrattiniC2×D4C22×#595
FittingC2×C17×#99C4
socleC22×C17#342
prime radicalC22×D4×D17C22
cosocleC2×D4×D17C23
hypercenterC2×#99#595
hypocenterC17C2×#1390
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095808);