Finite Group Databasebeta

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C2×C3×C5×C11×C32 #72189149

order10560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C11×C32
multiplicative(ℤ/10943)ˣ, (ℤ/11737)ˣ, (ℤ/15843)ˣ, (ℤ/21124)ˣ, (ℤ/21886)ˣ, (ℤ/23474)ˣ, (ℤ/31686)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C3×C5×C11
socle, prime radicalC22×C3×C5×C11C16
LCSG ▷ C1
UCSC1 ◁ G

136 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×C5×C11×C64, C3×C4×C5×C11×C32, C22×C3×C5×C11×C32, …
maximal normal subgroup ofC2×C3×C5×C11×C64, C3×C4×C5×C11×C32, C22×C3×C5×C11×C32, …
maximal quotient ofC2×C3×C5×C11×C64, C3×C4×C5×C11×C32, C22×C3×C5×C11×C32, …
automorphism group ofC31×C353
outer automorphism group ofC31×C353

GAP

Past the SmallGroups library coverage — no SmallGroups id.