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C22×C3×C42×C7×C9 #72190490

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 95551488
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C42×C7×C9
multiplicative(ℤ/19285)ˣ, (ℤ/21489)ˣ, (ℤ/22533)ˣ, (ℤ/23865)ˣ, (ℤ/24765)ˣ, (ℤ/24795)ˣ, (ℤ/25456)ˣ, (ℤ/26416)ˣ, (ℤ/27195)ˣ, (ℤ/27405)ˣ, (ℤ/28652)ˣ, (ℤ/29008)ˣ, (ℤ/30044)ˣ, (ℤ/31820)ˣ, (ℤ/33020)ˣ, (ℤ/36260)ˣ, (ℤ/38570)ˣ, (ℤ/38628)ˣ, (ℤ/40716)ˣ, (ℤ/42978)ˣ, (ℤ/45066)ˣ, (ℤ/47730)ˣ, (ℤ/49530)ˣ, (ℤ/49590)ˣ, (ℤ/54390)ˣ, (ℤ/54810)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C24×C32×C7
socle, prime radicalC24×C32×C7C22×C3
LCSG ▷ C1
UCSC1 ◁ G

4980 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C7×C8×C9, C2×C3×C43×C7×C9, C23×C3×C42×C7×C9
maximal normal subgroup ofC22×C3×C4×C7×C8×C9, C2×C3×C43×C7×C9, C23×C3×C42×C7×C9
maximal quotient ofC22×C3×C4×C7×C8×C9, C2×C3×C43×C7×C9, C23×C3×C42×C7×C9
automorphism group ofC16×C37×C43, C13×C16×C127, C5×C7×C27×C29, …
outer automorphism group ofC16×C37×C43, C13×C16×C127, C5×C7×C27×C29, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.