Finite Group Databasebeta

← Prev (#37529087) Next (#37529089) →

C2×C3×D643⋊C3 #37529088

order23148
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D643⋊C3
unambiguous semidirect productD643⋊(C2×C32)
unambiguous semidirect product(C643⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D643)⋊C32
unambiguous semidirect product(C2×C643⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D643)⋊C3

Splittings

Fitting, socleC2×C3×C643 ⋊ C2×C3
derived, SylowC643 ⋊ C22×C32
HallC3×C643⋊C3 ⋊ C22
HallC2×D643 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D643⋊C3
commutator, cosocle, hypocenterC643C22×C32
FrattiniC1G
Fitting, socleC2×C3×C643C2×C3
LCSG ▷ C643
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3858

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23148, 29);