Finite Group Databasebeta

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C24×C3×C42×C11 #72187331

order8448
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2536715059200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C214×C4

Aliases

abelianC24×C3×C42×C11
multiplicative(ℤ/35880)ˣ, (ℤ/38640)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C26×C3×C11
socle, prime radicalC26×C3×C11C22
LCSG ▷ C1
UCSC1 ◁ G

48060 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8448 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C4×C8×C11, C23×C3×C43×C11, C25×C3×C42×C11, …
maximal normal subgroup ofC24×C3×C4×C8×C11, C23×C3×C43×C11, C25×C3×C42×C11, …
maximal quotient ofC24×C3×C4×C8×C11, C23×C3×C43×C11, C25×C3×C42×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.