Finite Group Databasebeta

C2×#14537552 #17898344

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

Aliases

direct productC2×#14537552

Splittings

FittingC2×C17×#416 ⋊ C2
SylowC17 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#416C2
socleC23×C17C22×D4
prime radicalC22×#10587636C2
cosocleC2×C4×C17C25
hypercenterC2×#416D17
hypocenterC17C2×C4×#135
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

2894 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, 1033588);