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C22×C3×C4×C13×C25 #72193632

order15600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 92160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C13×C25
multiplicative(ℤ/23937)ˣ, (ℤ/24009)ˣ, (ℤ/27321)ˣ, (ℤ/29265)ˣ, (ℤ/29625)ˣ, (ℤ/31216)ˣ, (ℤ/31916)ˣ, (ℤ/32012)ˣ, (ℤ/36428)ˣ, (ℤ/39020)ˣ, (ℤ/39500)ˣ, (ℤ/46836)ˣ, (ℤ/47874)ˣ, (ℤ/48018)ˣ, (ℤ/54642)ˣ, (ℤ/58530)ˣ, (ℤ/59250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C23×C3×C5×C13
socle, prime radicalC23×C3×C5×C13C2×C5
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C13×C25, C2×C3×C42×C13×C25, C23×C3×C4×C13×C25
maximal normal subgroup ofC22×C3×C8×C13×C25, C2×C3×C42×C13×C25, C23×C3×C4×C13×C25
maximal quotient ofC22×C3×C8×C13×C25, C2×C3×C42×C13×C25, C23×C3×C4×C13×C25
automorphism group ofC3×C79×C125
outer automorphism group ofC3×C79×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.