Finite Group Databasebeta

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C22×C3×C27×C47 #72193242

order15228
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 89424
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C27×C47
multiplicative(ℤ/17773)ˣ, (ℤ/22851)ˣ, (ℤ/22923)ˣ, (ℤ/35546)ˣ, (ℤ/45702)ˣ, (ℤ/45846)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C32×C47
socle, prime radicalC22×C32×C47C9
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15228 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C27×C47, C23×C3×C27×C47
maximal normal subgroup ofC2×C3×C4×C27×C47, C23×C3×C27×C47
maximal quotient ofC2×C3×C4×C27×C47, C23×C3×C27×C47
automorphism group ofC7×C2539
outer automorphism group ofC7×C2539

GAP

Past the SmallGroups library coverage — no SmallGroups id.