Finite Group Databasebeta

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C24×C5×C121 #72188392

order9680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8870400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C5×C121
multiplicative(ℤ/31944)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC11C24×C5×C11
socle, prime radicalC24×C5×C11C11
LCSG ▷ C1
UCSC1 ◁ G

402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C121, C25×C5×C121, C24×C3×C5×C121
maximal normal subgroup ofC23×C4×C5×C121, C25×C5×C121, C24×C3×C5×C121
maximal quotient ofC23×C4×C5×C121, C25×C5×C121, C24×C3×C5×C121
automorphism group ofC3×C8×C1331
outer automorphism group ofC3×C8×C1331

GAP

Past the SmallGroups library coverage — no SmallGroups id.