Finite Group Databasebeta

← Prev (#72192571) Next (#72192573) →

C22×C32×C42×C25 #72192572

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 141557760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C32×C42×C25
multiplicative(ℤ/27573)ˣ, (ℤ/29445)ˣ, (ℤ/31408)ˣ, (ℤ/31815)ˣ, (ℤ/34125)ˣ, (ℤ/36764)ˣ, (ℤ/39260)ˣ, (ℤ/45500)ˣ, (ℤ/47268)ˣ, (ℤ/55146)ˣ, (ℤ/58500)ˣ, (ℤ/58890)ˣ, (ℤ/63630)ˣ, (ℤ/68250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C5C24×C32×C5
socle, prime radicalC24×C32×C5C22×C5
LCSG ▷ C1
UCSC1 ◁ G

4482 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C32×C4×C8×C25, C2×C32×C43×C25, C23×C32×C42×C25
maximal normal subgroup ofC22×C32×C4×C8×C25, C2×C32×C43×C25, C23×C32×C42×C25
maximal quotient ofC22×C32×C4×C8×C25, C2×C32×C43×C25, C23×C32×C42×C25
automorphism group ofC13×C16×C151
outer automorphism group ofC13×C16×C151

GAP

Past the SmallGroups library coverage — no SmallGroups id.