Finite Group Databasebeta

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C23×C3×C42×C23 #72187686

order8832
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2906652672
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C42×C23
multiplicative(ℤ/24440)ˣ, (ℤ/26320)ˣ, (ℤ/29328)ˣ, (ℤ/33240)ˣ, (ℤ/33360)ˣ, (ℤ/33840)ˣ, (ℤ/36660)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C25×C3×C23
socle, prime radicalC25×C3×C23C22
LCSG ▷ C1
UCSC1 ◁ G

6000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8832 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C8×C23, C22×C3×C43×C23, C24×C3×C42×C23, …
maximal normal subgroup ofC23×C3×C4×C8×C23, C22×C3×C43×C23, C24×C3×C42×C23, …
maximal quotient ofC23×C3×C4×C8×C23, C22×C3×C43×C23, C24×C3×C42×C23, …
automorphism group ofC5×C8×C13×C47, C5×C7×C16×C47, C3×C13×C16×C47
outer automorphism group ofC5×C8×C13×C47, C5×C7×C16×C47, C3×C13×C16×C47

GAP

Past the SmallGroups library coverage — no SmallGroups id.