Finite Group Databasebeta

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C23×C3×C11×C23 #72185240

order6072
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C11×C23
multiplicative(ℤ/7567)ˣ, (ℤ/9447)ˣ, (ℤ/9591)ˣ, (ℤ/9729)ˣ, (ℤ/11109)ˣ, (ℤ/12596)ˣ, (ℤ/12788)ˣ, (ℤ/14812)ˣ, (ℤ/15134)ˣ, (ℤ/18894)ˣ, (ℤ/19044)ˣ, (ℤ/19182)ˣ, (ℤ/19458)ˣ, (ℤ/22218)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C11×C23, C22×C3×C4×C11×C23, C23×C9×C11×C23, …
maximal normal subgroup ofC24×C3×C11×C23, C22×C3×C4×C11×C23, C23×C9×C11×C23, …
maximal quotient ofC24×C3×C11×C23, C22×C3×C4×C11×C23, C23×C9×C11×C23, …
automorphism group ofC7×C23×C47, C3×C47×C67, C3×C23×C139, …
outer automorphism group ofC7×C23×C47, C3×C47×C67, C3×C23×C139, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.