Finite Group Databasebeta

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C22×C5×C11×C32 #72186109

order7040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 61440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C5×C11×C32
multiplicative(ℤ/11649)ˣ, (ℤ/15488)ˣ, (ℤ/15532)ˣ, (ℤ/23298)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C23×C5×C11
socle, prime radicalC23×C5×C11C16
LCSG ▷ C1
UCSC1 ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C11×C64, C2×C4×C5×C11×C32, C23×C5×C11×C32, …
maximal normal subgroup ofC22×C5×C11×C64, C2×C4×C5×C11×C32, C23×C5×C11×C32, …
maximal quotient ofC22×C5×C11×C64, C2×C4×C5×C11×C32, C23×C5×C11×C32, …
automorphism group ofC121×C128
outer automorphism group ofC121×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.