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C2×C3×A4×3−1+2 #14519344

order1944
automorphism?
homologyAbelianization (H1) = C2×C34 · Schur multiplier (H2) = C2×C35

Aliases

direct productC2×C3×A4×3−1+2

Splittings

FittingC23×C3×3−1+2 ⋊ C3
SylowC23 ⋊ C32×3−1+2

Subgroups

subgroupG/H
centerC2×C32C32×A4
commutator, cosocleC22×C3C2×C34
FrattiniC3C2×C33×A4
FittingC23×C3×3−1+2C3
socleC23×C32C33
prime radicalC2×C33×A4C3
hypercenterC2×C3×3−1+2A4
hypocenterC22C2×C32×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C32 ◁ C2×C3×3−1+2

1304 conjugacy classes of subgroups; only the 532 normal subgroups are shown.

normal subgroups only

This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 532 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) = 162

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3738);