Finite Group Databasebeta

C2×#14542651 #17942404

order4352
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#14542651

Splittings

FittingC2×C17×#533 ⋊ C2
SylowC17 ⋊ C2×#3507

Subgroups

subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#533C2
socleC23×C17C25
prime radicalC2×#11763359C2
hypercenterC2×#533D17
hypocenterC17C2×#3507
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#533

7130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1077648);