Finite Group Databasebeta

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C23×C3×C293 #72186104

order7032
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 98112
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C293
multiplicative(ℤ/12327)ˣ, (ℤ/14072)ˣ, (ℤ/16436)ˣ, (ℤ/21108)ˣ, (ℤ/21132)ˣ, (ℤ/24654)ˣ

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7032 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C293, C24×C3×C293, C23×C9×C293, …
maximal normal subgroup ofC22×C3×C4×C293, C24×C3×C293, C23×C9×C293, …
maximal quotient ofC22×C3×C4×C293, C24×C3×C293, C23×C9×C293, …
automorphism group ofC3×C7×C587
outer automorphism group ofC3×C7×C587

GAP

Past the SmallGroups library coverage — no SmallGroups id.