Finite Group Databasebeta

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C4×C8×C11×C27 #72188240

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 23040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C8×C11×C27
multiplicative(ℤ/9701)ˣ, (ℤ/11885)ˣ, (ℤ/19402)ˣ, (ℤ/23770)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C9C22×C3×C11
socle, prime radicalC22×C3×C11C2×C4×C9
LCSG ▷ C1
UCSC1 ◁ G

176 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 ofC4×C11×C16×C27, C82×C11×C27, C2×C4×C8×C11×C27, …
maximal normal subgroup ofC4×C11×C16×C27, C82×C11×C27, C2×C4×C8×C11×C27, …
maximal quotient ofC4×C11×C16×C27, C82×C11×C27, C2×C4×C8×C11×C27, …
automorphism group ofC89×C109, C5×C2377
outer automorphism group ofC89×C109, C5×C2377

GAP

Past the SmallGroups library coverage — no SmallGroups id.