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C22×C4×C5×C7×C27 #72193153

order15120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 82944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C7×C27
multiplicative(ℤ/20845)ˣ, (ℤ/23217)ˣ, (ℤ/23577)ˣ, (ℤ/24981)ˣ, (ℤ/25839)ˣ, (ℤ/28425)ˣ, (ℤ/28755)ˣ, (ℤ/30956)ˣ, (ℤ/31436)ˣ, (ℤ/33308)ˣ, (ℤ/37900)ˣ, (ℤ/41690)ˣ, (ℤ/46434)ˣ, (ℤ/47154)ˣ, (ℤ/49962)ˣ, (ℤ/51678)ˣ, (ℤ/56850)ˣ, (ℤ/57510)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C23×C3×C5×C7
socle, prime radicalC23×C3×C5×C7C2×C9
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C7×C8×C27, C2×C42×C5×C7×C27, C23×C4×C5×C7×C27
maximal normal subgroup ofC22×C5×C7×C8×C27, C2×C42×C5×C7×C27, C23×C4×C5×C7×C27
maximal quotient ofC22×C5×C7×C8×C27, C2×C42×C5×C7×C27, C23×C4×C5×C7×C27
automorphism group ofC11×C29×C81, C5×C71×C81
outer automorphism group ofC11×C29×C81, C5×C71×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.