Finite Group Databasebeta

C2×#14543627 #17950617

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543627

Splittings

SylowC17 ⋊ C2×#1282

Subgroups

subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC22×C17C2×C4×C8
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17#95
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1282
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

1130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1085861);