Finite Group Databasebeta

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C23×C3×C4×C7×C16 #72189306

order10752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2113929216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C4×C7×C16
multiplicative(ℤ/27608)ˣ, (ℤ/29240)ˣ, (ℤ/31640)ˣ, (ℤ/33320)ˣ, (ℤ/35088)ˣ, (ℤ/35256)ˣ, (ℤ/35496)ˣ, (ℤ/37968)ˣ, (ℤ/38976)ˣ, (ℤ/39984)ˣ, (ℤ/40440)ˣ, (ℤ/40680)ˣ, (ℤ/41280)ˣ, (ℤ/41412)ˣ, (ℤ/43860)ˣ, (ℤ/47040)ˣ, (ℤ/47460)ˣ, (ℤ/49980)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C25×C3×C7
socle, prime radicalC25×C3×C7C2×C8
LCSG ▷ C1
UCSC1 ◁ G

12552 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C7×C32, C23×C3×C7×C8×C16, C22×C3×C42×C7×C16, …
maximal normal subgroup ofC23×C3×C4×C7×C32, C23×C3×C7×C8×C16, C22×C3×C42×C7×C16, …
maximal quotient ofC23×C3×C4×C7×C32, C23×C3×C7×C8×C16, C22×C3×C42×C7×C16, …
automorphism group ofC7×C8×C17×C29, C5×C8×C17×C43, C5×C7×C8×C113
outer automorphism group ofC7×C8×C17×C29, C5×C8×C17×C43, C5×C7×C8×C113

GAP

Past the SmallGroups library coverage — no SmallGroups id.