Finite Group Databasebeta

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C23×C3×C5×C8×C13 #72190825

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4128768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C5×C8×C13
multiplicative(ℤ/25912)ˣ, (ℤ/27544)ˣ, (ℤ/27808)ˣ, (ℤ/29176)ˣ, (ℤ/29344)ˣ, (ℤ/37512)ˣ, (ℤ/37728)ˣ, (ℤ/38868)ˣ, (ℤ/41316)ˣ, (ℤ/43764)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C3×C5×C13
socle, prime radicalC24×C3×C5×C13C4
LCSG ▷ C1
UCSC1 ◁ G

1352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C5×C13×C16, C24×C3×C5×C8×C13, C22×C3×C4×C5×C8×C13
maximal normal subgroup ofC23×C3×C5×C13×C16, C24×C3×C5×C8×C13, C22×C3×C4×C5×C8×C13
maximal quotient ofC23×C3×C5×C13×C16, C24×C3×C5×C8×C13, C22×C3×C4×C5×C8×C13
automorphism group ofC8×C41×C79, C8×C11×C313, C11×C32×C79, …
outer automorphism group ofC8×C41×C79, C8×C11×C313, C11×C32×C79, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.