Finite Group Databasebeta

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C4×C5×C9×C27 #72184271

order4860
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 69984
homologyAbelianization (H1) = G · Schur multiplier (H2) = C9

Aliases

abelianC4×C5×C9×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C9C2×C32×C5
socle, prime radicalC2×C32×C5C2×C3×C9
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C8×C9×C27, C2×C4×C5×C9×C27, C4×C5×C9×C81, …
maximal normal subgroup ofC5×C8×C9×C27, C2×C4×C5×C9×C27, C4×C5×C9×C81, …
maximal quotient ofC5×C8×C9×C27, C2×C4×C5×C9×C27, C4×C5×C9×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.