Finite Group Databasebeta

Q64×D107 #28338764

order13696
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ64×D107

Splittings

FittingQ64×C107 ⋊ C2
SylowC107 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D107
commutator, cosocleC16×C107C23
FrattiniC16C22×D107
FittingQ64×C107C2
socleC2×C107C2×D16
prime radicalC2×D107D16
hypercenterQ64D107
hypocenterC107C2×Q64
LCSG ▷ C16×C107 ▷ C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6848

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 6813);