Finite Group Databasebeta

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C22×C3×C4×C52×C9 #72189353

order10800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9953280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3×C5

Aliases

abelianC22×C3×C4×C52×C9
multiplicative(ℤ/12617)ˣ, (ℤ/12749)ˣ, (ℤ/13937)ˣ, (ℤ/14725)ˣ, (ℤ/16833)ˣ, (ℤ/17919)ˣ, (ℤ/18117)ˣ, (ℤ/20925)ˣ, (ℤ/22444)ˣ, (ℤ/25234)ˣ, (ℤ/25498)ˣ, (ℤ/27874)ˣ, (ℤ/29450)ˣ, (ℤ/33666)ˣ, (ℤ/35838)ˣ, (ℤ/36234)ˣ, (ℤ/41850)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C32×C52
socle, prime radicalC23×C32×C52C2×C3
LCSG ▷ C1
UCSC1 ◁ G

2160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C52×C8×C9, C2×C3×C42×C52×C9, C23×C3×C4×C52×C9, …
maximal normal subgroup ofC22×C3×C52×C8×C9, C2×C3×C42×C52×C9, C23×C3×C4×C52×C9, …
maximal quotient ofC22×C3×C52×C8×C9, C2×C3×C42×C52×C9, C23×C3×C4×C52×C9, …
automorphism group ofC11×C31×C37, C11×C19×C61, C7×C11×C181, …
outer automorphism group ofC11×C31×C37, C11×C19×C61, C7×C11×C181, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.