Finite Group Databasebeta

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C2×C43×C9×C11 #72191027

order12672
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 330301440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C43

Aliases

abelianC2×C43×C9×C11
multiplicative(ℤ/31760)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C3C24×C3×C11
socle, prime radicalC24×C3×C11C23×C3
LCSG ▷ C1
UCSC1 ◁ G

3816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C42×C8×C9×C11, C44×C9×C11, C22×C43×C9×C11
maximal normal subgroup ofC2×C42×C8×C9×C11, C44×C9×C11, C22×C43×C9×C11
maximal quotient ofC2×C42×C8×C9×C11, C44×C9×C11, C22×C43×C9×C11
automorphism group ofC5×C16×C397
outer automorphism group ofC5×C16×C397

GAP

Past the SmallGroups library coverage — no SmallGroups id.