Finite Group Databasebeta

C2×#14543834 #17960485

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14543834

Splittings

SylowC17 ⋊ C2×#1378

Subgroups

subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC22×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17#336
prime radicalC24×C17C2×C8
cosocleC22×#3622C23
hypercenterC2×#117#595
hypocenterC17C2×#1378
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

586 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, 1095729);