Finite Group Databasebeta

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C23×C4×C11×C27 #72188249

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3870720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C4×C11×C27
multiplicative(ℤ/20056)ˣ, (ℤ/29808)ˣ, (ℤ/30084)ˣ, (ℤ/37260)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C24×C3×C11
socle, prime radicalC24×C3×C11C2×C9
LCSG ▷ C1
UCSC1 ◁ G

944 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 ofC23×C8×C11×C27, C22×C42×C11×C27, C24×C4×C11×C27, …
maximal normal subgroup ofC23×C8×C11×C27, C22×C42×C11×C27, C24×C4×C11×C27, …
maximal quotient ofC23×C8×C11×C27, C22×C42×C11×C27, C24×C4×C11×C27, …
automorphism group ofC8×C23×C109, C16×C23×C81
outer automorphism group ofC8×C23×C109, C16×C23×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.