Finite Group Databasebeta

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C2×C42×C11×C27 #72188245

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 276480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C42×C11×C27
multiplicative(ℤ/12535)ˣ, (ℤ/25070)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C9C23×C3×C11
socle, prime radicalC23×C3×C11C22×C9
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C8×C11×C27, C43×C11×C27, C22×C42×C11×C27, …
maximal normal subgroup ofC2×C4×C8×C11×C27, C43×C11×C27, C22×C42×C11×C27, …
maximal quotient ofC2×C4×C8×C11×C27, C43×C11×C27, C22×C42×C11×C27, …
automorphism group ofC5×C23×C109
outer automorphism group ofC5×C23×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.