Finite Group Databasebeta

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C2×C3×C42×C7×C11 #72186397

order7392
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 184320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C7×C11
multiplicative(ℤ/8671)ˣ, (ℤ/9715)ˣ, (ℤ/17342)ˣ, (ℤ/19430)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C7×C11
socle, prime radicalC23×C3×C7×C11C22
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7392 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C7×C8×C11, C3×C43×C7×C11, C22×C3×C42×C7×C11, …
maximal normal subgroup ofC2×C3×C4×C7×C8×C11, C3×C43×C7×C11, C22×C3×C42×C7×C11, …
maximal quotient ofC2×C3×C4×C7×C8×C11, C3×C43×C7×C11, C22×C3×C42×C7×C11, …
automorphism group ofC13×C23×C29, C5×C29×C67
outer automorphism group ofC13×C23×C29, C5×C29×C67

GAP

Past the SmallGroups library coverage — no SmallGroups id.