Finite Group Databasebeta

D17×Q8⋊C16 #16944121

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

Aliases

direct productD17×Q8⋊C16

Splittings

FittingC17×Q8⋊C16 ⋊ C2
SylowC17 ⋊ C2×Q8⋊C16

Subgroups

subgroupG/H
centerC2×C8D4×D17
commutatorC4×C17C22×C16
FrattiniC4×C8C22×D17
FittingC17×Q8⋊C16C2
socleC22×C17C2×C22⋊C8
prime radicalC22×D17C22⋊C8
cosocleC4×C8×C17C23
hypercenterQ8⋊C16D17
hypocenterC17C2×Q8⋊C16
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

382 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, 79365);