Finite Group Databasebeta

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C24×C32×C7×C11 #72189608

order11088
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 58060800
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC24×C32×C7×C11
multiplicative(ℤ/20769)ˣ, (ℤ/23048)ˣ, (ℤ/25928)ˣ, (ℤ/26264)ˣ, (ℤ/27692)ˣ, (ℤ/33336)ˣ, (ℤ/34572)ˣ, (ℤ/35604)ˣ, (ℤ/38892)ˣ, (ℤ/39396)ˣ, (ℤ/40572)ˣ, (ℤ/41538)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

1608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11088 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C32×C4×C7×C11, C25×C32×C7×C11
maximal normal subgroup ofC23×C32×C4×C7×C11, C25×C32×C7×C11
maximal quotient ofC23×C32×C4×C7×C11, C25×C32×C7×C11
automorphism group ofC8×C43×C67, C7×C8×C463, C8×C49×C67
outer automorphism group ofC8×C43×C67, C7×C8×C463, C8×C49×C67

GAP

Past the SmallGroups library coverage — no SmallGroups id.