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C23×C3×C11×C53 #72192183

order13992
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 174720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C11×C53
multiplicative(ℤ/17227)ˣ, (ℤ/21507)ˣ, (ℤ/22149)ˣ, (ℤ/27992)ˣ, (ℤ/28676)ˣ, (ℤ/34454)ˣ, (ℤ/41988)ˣ, (ℤ/43014)ˣ, (ℤ/44298)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13992 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C11×C53, C22×C3×C4×C11×C53
maximal normal subgroup ofC24×C3×C11×C53, C22×C3×C4×C11×C53
maximal quotient ofC24×C3×C11×C53, C22×C3×C4×C11×C53
automorphism group ofC7×C23×C107
outer automorphism group ofC7×C23×C107

GAP

Past the SmallGroups library coverage — no SmallGroups id.