Finite Group Databasebeta

D17×#2148 #17187281

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD17×#2148

Splittings

FittingC17×#2148 ⋊ C2
SylowC17 ⋊ C2×#2148

Subgroups

subgroupG/H
centerC4#102×D17
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC17×#2148C2
socleC2×C17C22×#102
prime radicalC2×#135×D17C2
cosocleC2×C8×C17C24
hypercenter#2148D17
hypocenterC17C2×#2148
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2148

1154 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, 322525);