Finite Group Databasebeta

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C2×C5×C8×C9×C11 #72186828

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C8×C9×C11
multiplicative(ℤ/8159)ˣ, (ℤ/8833)ˣ, (ℤ/16318)ˣ, (ℤ/17666)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4C22×C3×C5×C11
socle, prime radicalC22×C3×C5×C11C3×C4
LCSG ▷ C1
UCSC1 ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C9×C11×C16, C4×C5×C8×C9×C11, C22×C5×C8×C9×C11, …
maximal normal subgroup ofC2×C5×C9×C11×C16, C4×C5×C8×C9×C11, C22×C5×C8×C9×C11, …
maximal quotient ofC2×C5×C9×C11×C16, C4×C5×C8×C9×C11, C22×C5×C8×C9×C11, …
automorphism group ofC41×C199, C73×C121
outer automorphism group ofC41×C199, C73×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.