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C3×C3⋊C8×3−1+2 #14517864

order1944
automorphism?
homologyAbelianization (H1) = C33×C8 · Schur multiplier (H2) = C32

Aliases

direct productC3×C3⋊C8×3−1+2
unambiguous semidirect productC3⋊(C3×C8×3−1+2)
unambiguous semidirect product(C9×C3⋊C8)⋊C32

Splittings

SylowC32×3−1+2 ⋊ C8

Subgroups

subgroupG/H
centerC32×C4C32×D3
commutatorC32C33×C8
FrattiniC3×C4C33×D3
FittingC32×C4×3−1+2C2
socleC2×C33C32×C4
prime radicalC2×C34C3×C4
cosocleC32×C4C2×C33
hypercenterC3×C4×3−1+2D3
hypocenterC3C3×C8×3−1+2
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C32×C4 ◁ C3×C4×3−1+2

622 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2258);