Finite Group Databasebeta

Q64×D113 #28392877

order14464
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ64×D113

Splittings

FittingQ64×C113 ⋊ C2
SylowC113 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D113
commutator, cosocleC16×C113C23
FrattiniC16C22×D113
FittingQ64×C113C2
socleC2×C113C2×D16
prime radicalC2×D113D16
hypercenterQ64D113
hypocenterC113C2×Q64
LCSG ▷ C16×C113 ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6813);