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C3×C4×C643⋊C3 #37529079

order23148
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C643⋊C3
unambiguous semidirect product(C4×C643)⋊C32
unambiguous semidirect product(C3×C4×C643)⋊C3

Splittings

FittingC3×C4×C643 ⋊ C3
derived, SylowC643 ⋊ C32×C4
HallC4×C643 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C4C643⋊C3
commutator, hypocenterC643C32×C4
FrattiniC2C2×C3×C643⋊C3
FittingC3×C4×C643C3
socleC2×C3×C643C2×C3
prime radicalC2×C3×C643⋊C3C2
cosocleC2×C643C2×C32
LCSG ▷ C643
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7716

Conjugacy classes & character table

2604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23148, 20);