Finite Group Databasebeta

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C3×C4×C9×C71 #72186580

order7668
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C4×C9×C71

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C2×C32×C71
socle, prime radicalC2×C32×C71C2×C3
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7668 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C8×C9×C71, C2×C3×C4×C9×C71, C3×C4×C27×C71, …
maximal normal subgroup ofC3×C8×C9×C71, C2×C3×C4×C9×C71, C3×C4×C27×C71, …
maximal quotient ofC3×C8×C9×C71, C2×C3×C4×C9×C71, C3×C4×C27×C71, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.