Finite Group Databasebeta

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C23×C3×C11×C29 #72186579

order7656
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 94080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C3×C11×C29
multiplicative(ℤ/9499)ˣ, (ℤ/11859)ˣ, (ℤ/12213)ˣ, (ℤ/15812)ˣ, (ℤ/18998)ˣ, (ℤ/23718)ˣ, (ℤ/24426)ˣ

Subgroups

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

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C11×C29, C24×C3×C11×C29, C23×C9×C11×C29, …
maximal normal subgroup ofC22×C3×C4×C11×C29, C24×C3×C11×C29, C23×C9×C11×C29, …
maximal quotient ofC22×C3×C4×C11×C29, C24×C3×C11×C29, C23×C9×C11×C29, …
automorphism group ofC7×C23×C59
outer automorphism group ofC7×C23×C59

GAP

Past the SmallGroups library coverage — no SmallGroups id.