Finite Group Databasebeta

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C22×C3×C5×C9×C13 #72186100

order7020
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 31104
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C5×C9×C13
multiplicative(ℤ/8197)ˣ, (ℤ/10539)ˣ, (ℤ/16394)ˣ, (ℤ/21078)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C22×C32×C5×C13
socle, prime radicalC22×C32×C5×C13C3
LCSG ▷ C1
UCSC1 ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7020 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C9×C13, C23×C3×C5×C9×C13, C22×C3×C5×C13×C27, …
maximal normal subgroup ofC2×C3×C4×C5×C9×C13, C23×C3×C5×C9×C13, C22×C3×C5×C13×C27, …
maximal quotient ofC2×C3×C4×C5×C9×C13, C23×C3×C5×C9×C13, C22×C3×C5×C13×C27, …
automorphism group ofC7×C1171, C9×C1171
outer automorphism group ofC7×C1171, C9×C1171

GAP

Past the SmallGroups library coverage — no SmallGroups id.