Finite Group Databasebeta

C2×#14531348 #17192837

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#14531348

Splittings

FittingC2×C17×#390 ⋊ C2
SylowC17 ⋊ C2×C4×#127

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#390C2
socleC24×C17C24
prime radicalC22×#10587626C2
cosocleC23×C17C25
hypercenterC2×#390D17
hypocenterC17C2×C4×#127
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#390

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328081);