Finite Group Databasebeta

D17×Q128 #16955372

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

Aliases

direct productD17×Q128

Splittings

FittingC17×Q128 ⋊ C2
SylowC17 ⋊ C2×Q128

Subgroups

subgroupG/H
centerC2D17×D32
commutator, cosocleC17×C32C23
FrattiniC32C22×D17
FittingC17×Q128C2
socleC2×C17C2×D32
prime radicalC2×D17D32
hypercenterQ128D17
hypocenterC17C2×Q128
LCSG ▷ C17×C32 ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ Q128

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90616);