Finite Group Databasebeta

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C23×C17×C27 #72183304

order3672
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 48384
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C17×C27
multiplicative(ℤ/7352)ˣ, (ℤ/11028)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C23×C3×C17
socle, prime radicalC23×C3×C17C9
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C17×C27, C24×C17×C27, C23×C17×C81, …
maximal normal subgroup ofC22×C4×C17×C27, C24×C17×C27, C23×C17×C81, …
maximal quotient ofC22×C4×C17×C27, C24×C17×C27, C23×C17×C81, …
automorphism group ofC8×C919, C3×C4×C919
outer automorphism group ofC8×C919, C3×C4×C919

GAP

Past the SmallGroups library coverage — no SmallGroups id.