Finite Group Databasebeta

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C22×C3×C4×C7×C41 #72191968

order13776
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C7×C41
multiplicative(ℤ/16849)ˣ, (ℤ/17845)ˣ, (ℤ/20335)ˣ, (ℤ/21663)ˣ, (ℤ/25845)ˣ, (ℤ/27568)ˣ, (ℤ/33698)ˣ, (ℤ/34460)ˣ, (ℤ/35690)ˣ, (ℤ/40670)ˣ, (ℤ/43326)ˣ, (ℤ/51690)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C7×C41
socle, prime radicalC23×C3×C7×C41C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13776 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C42×C7×C41, C22×C3×C7×C8×C41, C23×C3×C4×C7×C41
maximal normal subgroup ofC2×C3×C42×C7×C41, C22×C3×C7×C8×C41, C23×C3×C4×C7×C41
maximal quotient ofC2×C3×C42×C7×C41, C22×C3×C7×C8×C41, C23×C3×C4×C7×C41
automorphism group ofC5×C43×C83
outer automorphism group ofC5×C43×C83

GAP

Past the SmallGroups library coverage — no SmallGroups id.