Finite Group Databasebeta

← Prev (#13141449) Next (#13141451) →

C4×C8×(C3⋊D3)⋊C3 #13141450

order1728
isoclinismisoclinic class of (C3⋊D3)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C3×C4

Aliases

direct productC4×C8×(C3⋊D3)⋊C3
unambiguous semidirect product(C4×C8×C3⋊D3)⋊C3

Splittings

FittingC4×C8×H(3,𝔽3) ⋊ C2
derivedC32 ⋊ C2×C3×C4×C8
SylowH(3,𝔽3) ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC4×C8(C3⋊D3)⋊C3
commutator, hypocenterC32C2×C3×C4×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC4×C8×H(3,𝔽3)C2
socleC22×C3C2×C3×C4×D3
prime radicalC22×(C3⋊D3)⋊C3C2×C4
cosocleC2×C32×C4C23×C3
LCSG ▷ C32
UCSC1 ◁ C4×C8

611 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 7513);