Finite Group Databasebeta

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C24×C5×C89 #72186170

order7120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7096320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C5×C89
multiplicative(ℤ/15752)ˣ, (ℤ/23628)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C89, C25×C5×C89, C24×C3×C5×C89
maximal normal subgroup ofC23×C4×C5×C89, C25×C5×C89, C24×C3×C5×C89
maximal quotient ofC23×C4×C5×C89, C25×C5×C89, C24×C3×C5×C89
automorphism group ofC8×C11×C179
outer automorphism group ofC8×C11×C179

GAP

Past the SmallGroups library coverage — no SmallGroups id.