Finite Group Databasebeta

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C22×C4×C5×C7×C11 #72185362

order6160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C7×C11
multiplicative(ℤ/7337)ˣ, (ℤ/8165)ˣ, (ℤ/10527)ˣ, (ℤ/14036)ˣ, (ℤ/14674)ˣ, (ℤ/16330)ˣ, (ℤ/21054)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C5×C7×C11
socle, prime radicalC23×C5×C7×C11C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C7×C8×C11, C2×C42×C5×C7×C11, C23×C4×C5×C7×C11, …
maximal normal subgroup ofC22×C5×C7×C8×C11, C2×C42×C5×C7×C11, C23×C4×C5×C7×C11, …
maximal quotient ofC22×C5×C7×C8×C11, C2×C42×C5×C7×C11, C23×C4×C5×C7×C11, …
automorphism group ofC11×C23×C29, C5×C23×C71, C3×C29×C121
outer automorphism group ofC11×C23×C29, C5×C23×C71, C3×C29×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.