Finite Group Databasebeta

Q16×D101 #15692271

order3232
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ16×D101

Splittings

FittingQ16×C101 ⋊ C2
SylowC101 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC2D4×D101
commutator, cosocleC4×C101C23
FrattiniC4C22×D101
FittingQ16×C101C2
socleC2×C101C2×D4
prime radicalC2×D101D4
hypercenterQ16D101
hypocenterC101C2×Q16
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C4 ◁ Q16

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 162);