Finite Group Databasebeta

D17×#2102 #17064287

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

Aliases

direct productD17×#2102

Splittings

FittingC17×#2102 ⋊ C2
SylowC17 ⋊ C2×#2102

Subgroups

subgroupG/H
centerC4#124×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC17×#2102C2
socleC2×C17C2×#400
prime radicalC23×D17#41
hypercenter#2102D17
hypocenterC17C2×#2102
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2102

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 199531);