Finite Group Databasebeta

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C3×C4×C8×A4 #11919516

order1152
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C4×C8 · Schur multiplier (H2) = C2×C3×C4

Aliases

direct productC3×C4×C8×A4
unambiguous semidirect product(C22×C4×C8)⋊C32
unambiguous semidirect product(C22×C3×C4×C8)⋊C3

Splittings

FittingC22×C3×C4×C8 ⋊ C3
derivedC22 ⋊ C32×C4×C8
SylowC22×C4×C8 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C4×C8A4
commutator, hypocenterC22C32×C4×C8
FrattiniC2×C4C22×C3×A4
FittingC22×C3×C4×C8C3
socleC24×C3C2×C3×C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C4C22×C32
LCSG ▷ C22
UCSC1 ◁ C3×C4×C8

488 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 288

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153527);