Finite Group Databasebeta

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C23×C92×C11 #72186186

order7128
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6531840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C9

Aliases

abelianC23×C92×C11
multiplicative(ℤ/11343)ˣ, (ℤ/11799)ˣ, (ℤ/15124)ˣ, (ℤ/21492)ˣ, (ℤ/22686)ˣ, (ℤ/23598)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C23×C32×C11
socle, prime radicalC23×C32×C11C32
LCSG ▷ C1
UCSC1 ◁ G

736 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7128 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C92×C11, C24×C92×C11, C23×C9×C11×C27, …
maximal normal subgroup ofC22×C4×C92×C11, C24×C92×C11, C23×C9×C11×C27, …
maximal quotient ofC22×C4×C92×C11, C24×C92×C11, C23×C9×C11×C27, …
automorphism group ofC19×C23×C27, C4×C27×C199, C2×C19×C23×C27
outer automorphism group ofC19×C23×C27, C4×C27×C199, C2×C19×C23×C27

GAP

Past the SmallGroups library coverage — no SmallGroups id.