Finite Group Databasebeta

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C24×C4×C5×C7 #72182191

order2240
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 247726080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C4×C5×C7
multiplicative(ℤ/7656)ˣ, (ℤ/8520)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C5×C7
socle, prime radicalC25×C5×C7C2
LCSG ▷ C1
UCSC1 ◁ G

2724 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C5×C7×C8, C23×C42×C5×C7, C25×C4×C5×C7, …
maximal normal subgroup ofC24×C5×C7×C8, C23×C42×C5×C7, C25×C4×C5×C7, …
maximal quotient ofC24×C5×C7×C8, C23×C42×C5×C7, C25×C4×C5×C7, …
automorphism group ofC3×C8×C11×C29, C3×C5×C8×C71
outer automorphism group ofC3×C8×C11×C29, C3×C5×C8×C71

GAP

Past the SmallGroups library coverage — no SmallGroups id.