Finite Group Databasebeta

C2×#14530405 #17187014

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530405

Splittings

SylowC17 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C8C22⋊Dic17
commutatorC22×C17C23×C8
FrattiniC2×C8C23×D17
FittingC22×C17×#131C2
socleC22×C17C2×C22⋊C8
prime radicalC22×#41×C17C4
cosocleC2×C8×C17C24
hypercenterC22×#131D17
hypocenterC17C2×#2115
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×#131

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322258);