Finite Group Databasebeta

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C7×C11×C125 #72188347

order9625
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C4×C5×C25 (order 6000) · Inn(G) = C1 · Out(G) = C22×C3×C4×C5×C25
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC9625
abelianC7×C11×C125

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC25C5×C7×C11
socle, prime radicalC5×C7×C11C25
LCSG ▷ C1
UCSC1 ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9625 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic9625, C2×D9625
maximal subgroup ofC2×C7×C11×C125, C3×C7×C11×C125, D9625
maximal normal subgroup ofC2×C7×C11×C125, C3×C7×C11×C125, D9625
maximal quotient ofC2×C7×C11×C125, C3×C7×C11×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.