Finite Group Databasebeta

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C23×C23×C27 #72184346

order4968
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 66528
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C23×C27
multiplicative(ℤ/15228)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C23×C3×C23
socle, prime radicalC23×C3×C23C9
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C23×C27, C24×C23×C27, C23×C23×C81, …
maximal normal subgroup ofC22×C4×C23×C27, C24×C23×C27, C23×C23×C81, …
maximal quotient ofC22×C4×C23×C27, C24×C23×C27, C23×C23×C81, …
automorphism group ofC4×C47×C81
outer automorphism group ofC4×C47×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.