Finite Group Databasebeta

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C2×C3×C5×C16×C25 #72190407

order12000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 128000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C3×C5×C16×C25
multiplicative(ℤ/12431)ˣ, (ℤ/13211)ˣ, (ℤ/24862)ˣ, (ℤ/26422)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5×C8C22×C3×C52
socle, prime radicalC22×C3×C52C5×C8
LCSG ▷ C1
UCSC1 ◁ G

392 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×C5×C25×C32, C3×C4×C5×C16×C25, C22×C3×C5×C16×C25
maximal normal subgroup ofC2×C3×C5×C25×C32, C3×C4×C5×C16×C25, C22×C3×C5×C16×C25
maximal quotient ofC2×C3×C5×C25×C32, C3×C4×C5×C16×C25, C22×C3×C5×C16×C25
automorphism group ofC31×C401, C11×C1201
outer automorphism group ofC31×C401, C11×C1201

GAP

Past the SmallGroups library coverage — no SmallGroups id.