Finite Group Databasebeta

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C24×C5×C8×C11 #72186114

order7040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 825753600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C5×C8×C11
multiplicative(ℤ/22632)ˣ, (ℤ/23496)ˣ, (ℤ/24288)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C25×C5×C11
socle, prime radicalC25×C5×C11C4
LCSG ▷ C1
UCSC1 ◁ G

3952 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C5×C11×C16, C23×C4×C5×C8×C11, C25×C5×C8×C11, …
maximal normal subgroup ofC24×C5×C11×C16, C23×C4×C5×C8×C11, C25×C5×C8×C11, …
maximal quotient ofC24×C5×C11×C16, C23×C4×C5×C8×C11, C25×C5×C8×C11, …
automorphism group ofC3×C8×C23×C41, C3×C8×C11×C89, C3×C11×C23×C32
outer automorphism group ofC3×C8×C23×C41, C3×C8×C11×C89, C3×C11×C23×C32

GAP

Past the SmallGroups library coverage — no SmallGroups id.