Finite Group Databasebeta

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C3×C5×C82×C13 #72190822

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 147456
homologyAbelianization (H1) = G · Schur multiplier (H2) = C8

Aliases

abelianC3×C5×C82×C13
multiplicative(ℤ/12833)ˣ, (ℤ/25666)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C22×C3×C5×C13
socle, prime radicalC22×C3×C5×C13C42
LCSG ▷ C1
UCSC1 ◁ G

296 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C8×C13×C16, C2×C3×C5×C82×C13
maximal normal subgroup ofC3×C5×C8×C13×C16, C2×C3×C5×C82×C13
maximal quotient ofC3×C5×C8×C13×C16, C2×C3×C5×C82×C13
automorphism group ofC41×C313
outer automorphism group ofC41×C313

GAP

Past the SmallGroups library coverage — no SmallGroups id.