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C22×C3×C42×C5×C13 #72190827

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 14155776
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C3×C42×C5×C13
multiplicative(ℤ/20405)ˣ, (ℤ/22737)ˣ, (ℤ/24645)ˣ, (ℤ/25545)ˣ, (ℤ/25864)ˣ, (ℤ/25905)ˣ, (ℤ/26235)ˣ, (ℤ/26288)ˣ, (ℤ/27248)ˣ, (ℤ/27632)ˣ, (ℤ/27825)ˣ, (ℤ/27885)ˣ, (ℤ/29744)ˣ, (ℤ/30316)ˣ, (ℤ/31400)ˣ, (ℤ/31600)ˣ, (ℤ/32860)ˣ, (ℤ/33800)ˣ, (ℤ/34060)ˣ, (ℤ/34540)ˣ, (ℤ/37100)ˣ, (ℤ/37180)ˣ, (ℤ/38796)ˣ, (ℤ/40810)ˣ, (ℤ/45474)ˣ, (ℤ/47100)ˣ, (ℤ/47700)ˣ, (ℤ/49290)ˣ, (ℤ/50700)ˣ, (ℤ/51090)ˣ, (ℤ/51810)ˣ, (ℤ/52470)ˣ, (ℤ/55650)ˣ, (ℤ/55770)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C3×C5×C13
socle, prime radicalC24×C3×C5×C13C22
LCSG ▷ C1
UCSC1 ◁ G

1992 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 ofC22×C3×C4×C5×C8×C13, C2×C3×C43×C5×C13, C23×C3×C42×C5×C13
maximal normal subgroup ofC22×C3×C4×C5×C8×C13, C2×C3×C43×C5×C13, C23×C3×C42×C5×C13
maximal quotient ofC22×C3×C4×C5×C8×C13, C2×C3×C43×C5×C13, C23×C3×C42×C5×C13
automorphism group ofC8×C53×C61, C16×C31×C53, C13×C16×C131, …
outer automorphism group ofC8×C53×C61, C16×C31×C53, C13×C16×C131, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.