Finite Group Databasebeta

← Prev (#13142489) Next (#13142491) →

C22⋊C4×(C3⋊Dic3)⋊C3 #13142490

order1728
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C3×C4

Aliases

direct productC22⋊C4×(C3⋊Dic3)⋊C3
unambiguous semidirect product(C22⋊C4×C3⋊Dic3)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC23C22×(C3⋊D3)⋊C3
commutatorC2×C32C2×C3×C42
Frattini, socleC23×C3C22×C3×D3
FittingC2×C22⋊C4×H(3,𝔽3)C2
prime radicalC24×H(3,𝔽3)C22
cosocleC23×C32C23×C3
hypercenterC2×C22⋊C4(C3⋊D3)⋊C3
hypocenterC32C3×C4×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

1035 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8553);