Finite Group Databasebeta

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C23×C3×C5×C8×C11 #72189154

order10560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3440640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C5×C8×C11
multiplicative(ℤ/19803)ˣ, (ℤ/20559)ˣ, (ℤ/21976)ˣ, (ℤ/22072)ˣ, (ℤ/22816)ˣ, (ℤ/23584)ˣ, (ℤ/26404)ˣ, (ℤ/27104)ˣ, (ℤ/27412)ˣ, (ℤ/31704)ˣ, (ℤ/31776)ˣ, (ℤ/32964)ˣ, (ℤ/33108)ˣ, (ℤ/33948)ˣ, (ℤ/34848)ˣ, (ℤ/35244)ˣ, (ℤ/39606)ˣ, (ℤ/41118)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C3×C5×C11
socle, prime radicalC24×C3×C5×C11C4
LCSG ▷ C1
UCSC1 ◁ G

1352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C5×C11×C16, C24×C3×C5×C8×C11, C22×C3×C4×C5×C8×C11, …
maximal normal subgroup ofC23×C3×C5×C11×C16, C24×C3×C5×C8×C11, C22×C3×C4×C5×C8×C11, …
maximal quotient ofC23×C3×C5×C11×C16, C24×C3×C5×C8×C11, C22×C3×C4×C5×C8×C11, …
automorphism group ofC8×C41×C67, C8×C31×C89, C23×C31×C32, …
outer automorphism group ofC8×C41×C67, C8×C31×C89, C23×C31×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.