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C2×C3×C4×C5×C8×C11 #72189153

order10560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 163840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C4×C5×C8×C11
multiplicative(ℤ/12259)ˣ, (ℤ/12727)ˣ, (ℤ/13735)ˣ, (ℤ/13795)ˣ, (ℤ/15575)ˣ, (ℤ/16287)ˣ, (ℤ/19815)ˣ, (ℤ/20025)ˣ, (ℤ/21136)ˣ, (ℤ/21152)ˣ, (ℤ/21716)ˣ, (ℤ/24518)ˣ, (ℤ/25454)ˣ, (ℤ/26420)ˣ, (ℤ/27470)ˣ, (ℤ/27590)ˣ, (ℤ/31150)ˣ, (ℤ/32574)ˣ, (ℤ/39630)ˣ, (ℤ/40050)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C3×C5×C11
socle, prime radicalC23×C3×C5×C11C2×C4
LCSG ▷ C1
UCSC1 ◁ G

648 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 ofC2×C3×C4×C5×C11×C16, C2×C3×C5×C82×C11, C3×C42×C5×C8×C11, …
maximal normal subgroup ofC2×C3×C4×C5×C11×C16, C2×C3×C5×C82×C11, C3×C42×C5×C8×C11, …
maximal quotient ofC2×C3×C4×C5×C11×C16, C2×C3×C5×C82×C11, C3×C42×C5×C8×C11, …
automorphism group ofC13×C23×C41
outer automorphism group ofC13×C23×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.