Finite Group Databasebeta

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C23×C3×C4×C7×C8 #72184692

order5376
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1056964608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C4×C7×C8
multiplicative(ℤ/19488)ˣ, (ℤ/20640)ˣ, (ℤ/23520)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C25×C3×C7
socle, prime radicalC25×C3×C7C2×C4
LCSG ▷ C1
UCSC1 ◁ G

9276 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5376 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C7×C16, C23×C3×C7×C82, C22×C3×C42×C7×C8, …
maximal normal subgroup ofC23×C3×C4×C7×C16, C23×C3×C7×C82, C22×C3×C42×C7×C8, …
maximal quotient ofC23×C3×C4×C7×C16, C23×C3×C7×C82, C22×C3×C42×C7×C8, …
automorphism group ofC3×C7×C29×C32, C3×C5×C32×C43, C3×C5×C32×C49
outer automorphism group ofC3×C7×C29×C32, C3×C5×C32×C43, C3×C5×C32×C49

GAP

Past the SmallGroups library coverage — no SmallGroups id.