Finite Group Databasebeta

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C3×C4×C8×C125 #72190409

order12000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 25600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C8×C125
multiplicative(ℤ/15005)ˣ, (ℤ/30010)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C25C22×C3×C5
socle, prime radicalC22×C3×C5C2×C4×C25
LCSG ▷ C1
UCSC1 ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C16×C125, C3×C82×C125, C2×C3×C4×C8×C125
maximal normal subgroup ofC3×C4×C16×C125, C3×C82×C125, C2×C3×C4×C8×C125
maximal quotient ofC3×C4×C16×C125, C3×C82×C125, C2×C3×C4×C8×C125
automorphism group ofC5×C3001
outer automorphism group ofC5×C3001

GAP

Past the SmallGroups library coverage — no SmallGroups id.