Finite Group Databasebeta

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C24×C52×C8 #72182943

order3200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9909043200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C5

Aliases

abelianC24×C52×C8
multiplicative(ℤ/10824)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C25×C52
socle, prime radicalC25×C52C4
LCSG ▷ C1
UCSC1 ◁ G

7904 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C52×C16, C23×C4×C52×C8, C25×C52×C8, …
maximal normal subgroup ofC24×C52×C16, C23×C4×C52×C8, C25×C52×C8, …
maximal quotient ofC24×C52×C16, C23×C4×C52×C8, C25×C52×C8, …
automorphism group ofC3×C8×C11×C41
outer automorphism group ofC3×C8×C11×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.