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2−1+4×(C3⋊D3)⋊C3 #13164959

order1728
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C3

Aliases

direct product2−1+4×(C3⋊D3)⋊C3

Splittings

FittingH(3,𝔽3)×2−1+4 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×2−1+4

Subgroups

subgroupG/H
centerC2C24×(C3⋊D3)⋊C3
commutator, cosocleC2×C32C25×C3
Frattini, socleC2×C3C24×C3×D3
FittingH(3,𝔽3)×2−1+4C2
hypercenter2−1+4(C3⋊D3)⋊C3
hypocenterC32C2×C3×2−1+4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ 2−1+4

2925 conjugacy classes of subgroups; only the 958 normal subgroups are shown.

normal subgroups only

This group has 2925 conjugacy classes of subgroups — too many to draw. Only its 958 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) = 144

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 31022);