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C3×(C43⋊C3)⋊C49 #34038902

order18963
automorphism?
homologyAbelianization (H1) = C32×C49 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C43⋊C3)⋊C49
unambiguous semidirect product(C43⋊C3)⋊(C3×C49)
unambiguous semidirect product(C3×C43⋊C3)⋊C49
unambiguous semidirect product(C43⋊C49)⋊C32
unambiguous semidirect product(C3×C43⋊C49)⋊C3

Splittings

derived, SylowC43 ⋊ C32×C49
HallC43⋊C49 ⋊ C32
HallC3×C43⋊C3 ⋊ C49

Subgroups

subgroupG/H
center, hypercenterC3×C7(C43⋊C3)⋊C7
commutator, hypocenterC43C32×C49
FrattiniC7C3×(C43⋊C3)⋊C7
Fitting, socleC3×C7×C43C3×C7
prime radicalC3×C7×C43⋊C3C7
cosocleC7×C43C32×C7
LCSG ▷ C43
UCSC1 ◁ C3×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6321

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×(D43⋊C3)⋊C49, C3⋊((D43⋊C3)⋊C49), D3×(C43⋊C3)⋊C49, …
maximal normal subgroup ofC3×(D43⋊C3)⋊C49, C3⋊((D43⋊C3)⋊C49), D3×(C43⋊C3)⋊C49, …
maximal quotient ofC2×C3×(C43⋊C3)⋊C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18963, 9);