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C2×C3×C5×C8×C25 #72185196

order6000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 64000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C3×C5×C8×C25
multiplicative(ℤ/6191)ˣ, (ℤ/6611)ˣ, (ℤ/12382)ˣ, (ℤ/13222)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C5C22×C3×C52
socle, prime radicalC22×C3×C52C4×C5
LCSG ▷ C1
UCSC1 ◁ G

308 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C16×C25, C3×C4×C5×C8×C25, C22×C3×C5×C8×C25, …
maximal normal subgroup ofC2×C3×C5×C16×C25, C3×C4×C5×C8×C25, C22×C3×C5×C8×C25, …
maximal quotient ofC2×C3×C5×C16×C25, C3×C4×C5×C8×C25, C22×C3×C5×C8×C25, …
automorphism group ofC41×C151, C11×C601
outer automorphism group ofC41×C151, C11×C601

GAP

Past the SmallGroups library coverage — no SmallGroups id.