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C2×C3×C5×C8×C9 #72182146

order2160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6912
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C3×C5×C8×C9
multiplicative(ℤ/2263)ˣ, (ℤ/4526)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4C22×C32×C5
socle, prime radicalC22×C32×C5C3×C4
LCSG ▷ C1
UCSC1 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C9×C16, C3×C4×C5×C8×C9, C22×C3×C5×C8×C9, …
maximal normal subgroup ofC2×C3×C5×C9×C16, C3×C4×C5×C8×C9, C22×C3×C5×C8×C9, …
maximal quotient ofC2×C3×C5×C9×C16, C3×C4×C5×C8×C9, C22×C3×C5×C8×C9, …
automorphism group ofC31×C73, C2×C31×C73
outer automorphism group ofC31×C73, C2×C31×C73

GAP

Past the SmallGroups library coverage — no SmallGroups id.