Finite Group Databasebeta

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C24×C3×C13×C23 #72192514

order14352
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10644480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C13×C23
multiplicative(ℤ/29704)ˣ, (ℤ/33544)ˣ, (ℤ/43128)ˣ, (ℤ/44556)ˣ, (ℤ/50316)ˣ

Subgroups

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

536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C3×C13×C23, C23×C3×C4×C13×C23
maximal normal subgroup ofC25×C3×C13×C23, C23×C3×C4×C13×C23
maximal quotient ofC25×C3×C13×C23, C23×C3×C4×C13×C23
automorphism group ofC8×C47×C79
outer automorphism group ofC8×C47×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.