Finite Group Databasebeta

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C23×C42×C5×C11 #72186117

order7040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2642411520
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C42×C5×C11
multiplicative(ℤ/20240)ˣ, (ℤ/27600)ˣ, (ℤ/29040)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C25×C5×C11
socle, prime radicalC25×C5×C11C22
LCSG ▷ C1
UCSC1 ◁ G

6000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C8×C11, C22×C43×C5×C11, C24×C42×C5×C11, …
maximal normal subgroup ofC23×C4×C5×C8×C11, C22×C43×C5×C11, C24×C42×C5×C11, …
maximal quotient ofC23×C4×C5×C8×C11, C22×C43×C5×C11, C24×C42×C5×C11, …
automorphism group ofC5×C11×C16×C23, C3×C16×C23×C25, C3×C5×C16×C121
outer automorphism group ofC5×C11×C16×C23, C3×C16×C23×C25, C3×C5×C16×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.