Finite Group Databasebeta

C2×#14543830 #17960475

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

Aliases

direct productC2×#14543830

Splittings

FittingC2×C17×M32 ⋊ C4
SylowC17 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC22×C17C2×C4×C8
FrattiniC2×C8C22×#595
FittingC2×C17×M32C4
socleC22×C17#336
prime radicalC23×D17C2×C8
cosocleC2×C8×D17C23
hypercenterC2×M32#595
hypocenterC17C2×#1377
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1095719);