Finite Group Databasebeta

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C2×C3×C16×C125 #72190406

order12000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C16×C125
multiplicative(ℤ/12767)ˣ, (ℤ/25534)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C25C22×C3×C5
socle, prime radicalC22×C3×C5C8×C25
LCSG ▷ C1
UCSC1 ◁ G

112 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 ofC2×C3×C32×C125, C3×C4×C16×C125, C22×C3×C16×C125
maximal normal subgroup ofC2×C3×C32×C125, C3×C4×C16×C125, C22×C3×C16×C125
maximal quotient ofC2×C3×C32×C125, C3×C4×C16×C125, C22×C3×C16×C125
automorphism group ofC17×C751
outer automorphism group ofC17×C751

GAP

Past the SmallGroups library coverage — no SmallGroups id.