Finite Group Databasebeta

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C4×C7×C9×C3⋊C8 #72219183

order6048
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C7×C8×C9 · Schur multiplier (H2) = C4

Aliases

direct productC4×C7×C9×C3⋊C8

Splittings

derivedC3 ⋊ C4×C7×C8×C9
HallC3×C7×C9 ⋊ C4×C8
SylowC3×C9 ⋊ C4×C7×C8

Subgroups

subgroupG/H
center, hypercenterC42×C7×C9D3
commutator, hypocenterC3C4×C7×C8×C9
FrattiniC2×C3×C4C2×C3×D3×C7
FittingC3×C42×C7×C9C2
socle, prime radicalC22×C32×C7C2×C3×C4
cosocleC2×C32×C4C22×C3×C7
LCSG ▷ C3
UCSC1 ◁ C42×C7×C9

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×D3×C7×C8×C9
maximal normal subgroup ofC4×D3×C7×C8×C9

GAP

Past the SmallGroups library coverage — no SmallGroups id.