Finite Group Databasebeta

← Prev (#11922938) Next (#11922940) →

D4×C3⋊#226 #11922939

order1152
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23×C3

Aliases

direct productD4×C3⋊#226

Subgroups

subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FittingC3×D4×Q8D3
socleC22×C3C22×S4
prime radicalC3×D4×SL(2,𝔽3)C2
hypercenterC2×D4C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

698 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 87 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) = 192

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 156950);