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3−1+2×#634 #14518923

order1944
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C3

Aliases

direct product3−1+2×#634

Splittings

SylowC32×3−1+2 ⋊ Q8

Subgroups

subgroupG/H
center, FrattiniC2×C3C2×C32×C3⋊D3
commutator, socle, cosocleC2×C33C22×C32
FittingC32×C4×3−1+2C2
prime radicalC2×C34C22×C3
hypercenterC4×3−1+2C3⋊D3
hypocenterC32Q8×3−1+2
LCSG ▷ C2×C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C4×3−1+2

648 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 147 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

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3317);