Finite Group Databasebeta

D17×#1367 #16945864

order4352
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD17×#1367

Splittings

FittingC17×#1367 ⋊ C2
SylowC17 ⋊ C2×#1367

Subgroups

subgroupG/H
centerC2×C8D4×D17
commutatorC4×C17C22×C16
FrattiniC4×C8C22×D17
FittingC17×#1367C2
socleC22×C17C2×C4⋊C8
prime radicalC22×D17C4⋊C8
cosocleC4×C8×C17C23
hypercenter#1367D17
hypocenterC17C2×#1367
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ #1367

286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 81108);