Finite Group Databasebeta

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C2×C42×C5×C9×C11 #72193826

order15840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C42×C5×C9×C11
multiplicative(ℤ/20815)ˣ, (ℤ/21275)ˣ, (ℤ/21835)ˣ, (ℤ/22385)ˣ, (ℤ/29775)ˣ, (ℤ/39700)ˣ, (ℤ/41630)ˣ, (ℤ/42550)ˣ, (ℤ/43670)ˣ, (ℤ/44770)ˣ, (ℤ/59550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C23×C3×C5×C11
socle, prime radicalC23×C3×C5×C11C22×C3
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C8×C9×C11, C43×C5×C9×C11, C22×C42×C5×C9×C11
maximal normal subgroup ofC2×C4×C5×C8×C9×C11, C43×C5×C9×C11, C22×C42×C5×C9×C11
maximal quotient ofC2×C4×C5×C8×C9×C11, C43×C5×C9×C11, C22×C42×C5×C9×C11

GAP

Past the SmallGroups library coverage — no SmallGroups id.