Finite Group Databasebeta

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C24×C3×C7×C25 #72187286

order8400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4838400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C7×C25
multiplicative(ℤ/25224)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C24×C3×C5×C7
socle, prime radicalC24×C3×C5×C7C5
LCSG ▷ C1
UCSC1 ◁ G

804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C7×C25, C25×C3×C7×C25, C24×C7×C9×C25, …
maximal normal subgroup ofC23×C3×C4×C7×C25, C25×C3×C7×C25, C24×C7×C9×C25, …
maximal quotient ofC23×C3×C4×C7×C25, C25×C3×C7×C25, C24×C7×C9×C25, …
automorphism group ofC3×C8×C1051
outer automorphism group ofC3×C8×C1051

GAP

Past the SmallGroups library coverage — no SmallGroups id.