Finite Group Databasebeta

Q16×D113 #16813638

order3616
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ16×D113

Splittings

FittingQ16×C113 ⋊ C2
SylowC113 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC2D4×D113
commutator, cosocleC4×C113C23
FrattiniC4C22×D113
FittingQ16×C113C2
socleC2×C113C2×D4
prime radicalC2×D113D4
hypercenterQ16D113
hypocenterC113C2×Q16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C4 ◁ Q16

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3616, 162);