Finite Group Databasebeta

D17×#1788 #17033511

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD17×#1788

Splittings

FittingC17×#1788 ⋊ C2
SylowC17 ⋊ C2×#1788

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1788C2
socleC23×C17C22×D4
prime radicalC22×#41×D17C2
cosocleC22×C4×C17C24
hypercenter#1788D17
hypocenterC17C2×#1788
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

4070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 168755);