Finite Group Databasebeta

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C2×C3×C5×C13×C32 #72190820

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6144
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C13×C32
multiplicative(ℤ/12707)ˣ, (ℤ/13739)ˣ, (ℤ/14567)ˣ, (ℤ/18729)ˣ, (ℤ/25414)ˣ, (ℤ/27478)ˣ, (ℤ/29134)ˣ, (ℤ/37458)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C22×C3×C5×C13
socle, prime radicalC22×C3×C5×C13C16
LCSG ▷ C1
UCSC1 ◁ G

136 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 ofC2×C3×C5×C13×C64, C3×C4×C5×C13×C32, C22×C3×C5×C13×C32
maximal normal subgroup ofC2×C3×C5×C13×C64, C3×C4×C5×C13×C32, C22×C3×C5×C13×C32
maximal quotient ofC2×C3×C5×C13×C64, C3×C4×C5×C13×C32, C22×C3×C5×C13×C32
automorphism group ofC97×C131, C11×C1249, C7×C2081
outer automorphism group ofC97×C131, C11×C1249, C7×C2081

GAP

Past the SmallGroups library coverage — no SmallGroups id.