Finite Group Databasebeta

← Prev (#72188180) Next (#72188182) →

C22×C3×C42×C72 #72188181

order9408
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 594542592
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4×C7

Aliases

abelianC22×C3×C42×C72
multiplicative(ℤ/18705)ˣ, (ℤ/19952)ˣ, (ℤ/21315)ˣ, (ℤ/22736)ˣ, (ℤ/24940)ˣ, (ℤ/28420)ˣ, (ℤ/37410)ˣ, (ℤ/42630)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C3×C72
socle, prime radicalC24×C3×C72C22
LCSG ▷ C1
UCSC1 ◁ G

4980 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9408 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C72×C8, C2×C3×C43×C72, C23×C3×C42×C72, …
maximal normal subgroup ofC22×C3×C4×C72×C8, C2×C3×C43×C72, C23×C3×C42×C72, …
maximal quotient ofC22×C3×C4×C72×C8, C2×C3×C43×C72, C23×C3×C42×C72, …
automorphism group ofC16×C29×C43, C16×C29×C49
outer automorphism group ofC16×C29×C43, C16×C29×C49

GAP

Past the SmallGroups library coverage — no SmallGroups id.