Finite Group Databasebeta

← Prev (#72189944) Next (#72189946) →

C2×C32×C4×C5×C32 #72189945

order11520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1572864
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C32×C4×C5×C32
multiplicative(ℤ/13871)ˣ, (ℤ/15035)ˣ, (ℤ/16975)ˣ, (ℤ/17751)ˣ, (ℤ/21825)ˣ, (ℤ/23668)ˣ, (ℤ/27742)ˣ, (ℤ/30070)ˣ, (ℤ/33950)ˣ, (ℤ/35502)ˣ, (ℤ/43650)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C23×C32×C5
socle, prime radicalC23×C32×C5C2×C16
LCSG ▷ C1
UCSC1 ◁ G

1620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C5×C64, C2×C32×C5×C8×C32, C32×C42×C5×C32, …
maximal normal subgroup ofC2×C32×C4×C5×C64, C2×C32×C5×C8×C32, C32×C42×C5×C32, …
maximal quotient ofC2×C32×C4×C5×C64, C2×C32×C5×C8×C32, C32×C42×C5×C32, …
automorphism group ofC11×C13×C97
outer automorphism group ofC11×C13×C97

GAP

Past the SmallGroups library coverage — no SmallGroups id.