Finite Group Databasebeta

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C24×C52×C13 #72184579

order5200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 116121600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C5

Aliases

abelianC24×C52×C13
multiplicative(ℤ/11528)ˣ, (ℤ/17292)ˣ

Subgroups

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

1072 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C52×C13, C25×C52×C13, C24×C3×C52×C13, …
maximal normal subgroup ofC23×C4×C52×C13, C25×C52×C13, C24×C3×C52×C13, …
maximal quotient ofC23×C4×C52×C13, C25×C52×C13, C24×C3×C52×C13, …
automorphism group ofC8×C11×C131
outer automorphism group ofC8×C11×C131

GAP

Past the SmallGroups library coverage — no SmallGroups id.