Finite Group Databasebeta

← Prev (#72190201) Next (#72190203) →

C22×C3×C4×C5×C72 #72190202

order11760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3096576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C7

Aliases

abelianC22×C3×C4×C5×C72
multiplicative(ℤ/13717)ˣ, (ℤ/14413)ˣ, (ℤ/15265)ˣ, (ℤ/15631)ˣ, (ℤ/17395)ˣ, (ℤ/18357)ˣ, (ℤ/18531)ˣ, (ℤ/24476)ˣ, (ℤ/27434)ˣ, (ℤ/28826)ˣ, (ℤ/30530)ˣ, (ℤ/31262)ˣ, (ℤ/34790)ˣ, (ℤ/36714)ˣ, (ℤ/37062)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C5×C72
socle, prime radicalC23×C3×C5×C72C2
LCSG ▷ C1
UCSC1 ◁ G

1080 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C72×C8, C2×C3×C42×C5×C72, C23×C3×C4×C5×C72
maximal normal subgroup ofC22×C3×C5×C72×C8, C2×C3×C42×C5×C72, C23×C3×C4×C5×C72
maximal quotient ofC22×C3×C5×C72×C8, C2×C3×C42×C5×C72, C23×C3×C4×C5×C72
automorphism group ofC11×C29×C43
outer automorphism group ofC11×C29×C43

GAP

Past the SmallGroups library coverage — no SmallGroups id.