Finite Group Databasebeta

Q64×D191 #37574823

order24448
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ64×D191

Splittings

FittingQ64×C191 ⋊ C2
SylowC191 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC2D16×D191
commutator, cosocleC16×C191C23
FrattiniC16C22×D191
FittingQ64×C191C2
socleC2×C191C2×D16
prime radicalC2×D191D16
hypercenterQ64D191
hypocenterC191C2×Q64
LCSG ▷ C16×C191 ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q64

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

1843 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6813);