Finite Group Databasebeta

D17×#1812 #17033962

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD17×#1812

Splittings

FittingC17×#1812 ⋊ C2
SylowC17 ⋊ C2×#1812

Subgroups

subgroupG/H
centerC4#117×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1812C2
socleC2×C17C2×#380
prime radicalC2×#41×D17C22
cosocleC22×C4×C17C24
hypercenter#1812D17
hypocenterC17C2×#1812
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×M16 ◁ #1812

1346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169206);