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C22×C3×C4×C7×C25 #72187285

order8400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C7×C25
multiplicative(ℤ/13029)ˣ, (ℤ/13137)ˣ, (ℤ/14721)ˣ, (ℤ/14847)ˣ, (ℤ/15765)ˣ, (ℤ/16125)ˣ, (ℤ/16816)ˣ, (ℤ/17372)ˣ, (ℤ/17516)ˣ, (ℤ/18375)ˣ, (ℤ/19628)ˣ, (ℤ/19796)ˣ, (ℤ/21020)ˣ, (ℤ/21500)ˣ, (ℤ/24500)ˣ, (ℤ/25236)ˣ, (ℤ/26058)ˣ, (ℤ/26274)ˣ, (ℤ/29442)ˣ, (ℤ/29694)ˣ, (ℤ/31530)ˣ, (ℤ/32250)ˣ, (ℤ/36750)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C23×C3×C5×C7
socle, prime radicalC23×C3×C5×C7C2×C5
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C7×C8×C25, C2×C3×C42×C7×C25, C23×C3×C4×C7×C25, …
maximal normal subgroup ofC22×C3×C7×C8×C25, C2×C3×C42×C7×C25, C23×C3×C4×C7×C25, …
maximal quotient ofC22×C3×C7×C8×C25, C2×C3×C42×C7×C25, C23×C3×C4×C7×C25, …
automorphism group ofC3×C43×C125, C3×C49×C125, C4×C43×C125, …
outer automorphism group ofC3×C43×C125, C3×C49×C125, C4×C43×C125, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.