Finite Group Databasebeta

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C22×C27×C73 #72186804

order7884
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7776
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C27×C73
multiplicative(ℤ/11829)ˣ, (ℤ/15772)ˣ, (ℤ/23658)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C3×C73
socle, prime radicalC22×C3×C73C9
LCSG ▷ C1
UCSC1 ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7884 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C27×C73, C23×C27×C73, C22×C73×C81, …
maximal normal subgroup ofC2×C4×C27×C73, C23×C27×C73, C22×C73×C81, …
maximal quotient ofC2×C4×C27×C73, C23×C27×C73, C22×C73×C81, …
automorphism group ofC3×C3943
outer automorphism group ofC3×C3943

GAP

Past the SmallGroups library coverage — no SmallGroups id.