Finite Group Databasebeta

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C22×C3×C7×C125 #72189111

order10500
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C3×C7×C125
multiplicative(ℤ/10793)ˣ, (ℤ/12299)ˣ, (ℤ/21586)ˣ, (ℤ/24598)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC25C22×C3×C5×C7
socle, prime radicalC22×C3×C5×C7C25
LCSG ▷ C1
UCSC1 ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C7×C125, C23×C3×C7×C125, C22×C7×C9×C125, …
maximal normal subgroup ofC2×C3×C4×C7×C125, C23×C3×C7×C125, C22×C7×C9×C125, …
maximal quotient ofC2×C3×C4×C7×C125, C23×C3×C7×C125, C22×C7×C9×C125, …
automorphism group ofC43×C251
outer automorphism group ofC43×C251

GAP

Past the SmallGroups library coverage — no SmallGroups id.