Finite Group Databasebeta

C2×#14543680 #17951493

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14543680

Splittings

FittingC2×C17×C4⋊C8 ⋊ C4
SylowC17 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC42C22×#595
FittingC2×C17×C4⋊C8C4
socleC23×C17#95
prime radicalC23×D17C22⋊C4
cosocleC42×D17C23
hypercenterC2×C4⋊C8#595
hypocenterC17C2×#1303
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086737);