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C22×C3×C5×C11×C16 #72189152

order10560
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 61440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C5×C11×C16
multiplicative(ℤ/12121)ˣ, (ℤ/12529)ˣ, (ℤ/14399)ˣ, (ℤ/16629)ˣ, (ℤ/16881)ˣ, (ℤ/18501)ˣ, (ℤ/18513)ˣ, (ℤ/21184)ˣ, (ℤ/22172)ˣ, (ℤ/22508)ˣ, (ℤ/24242)ˣ, (ℤ/24668)ˣ, (ℤ/25058)ˣ, (ℤ/28798)ˣ, (ℤ/31716)ˣ, (ℤ/33258)ˣ, (ℤ/33762)ˣ, (ℤ/37002)ˣ, (ℤ/37026)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C3×C5×C11
socle, prime radicalC23×C3×C5×C11C8
LCSG ▷ C1
UCSC1 ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C11×C32, C2×C3×C4×C5×C11×C16, C23×C3×C5×C11×C16, …
maximal normal subgroup ofC22×C3×C5×C11×C32, C2×C3×C4×C5×C11×C16, C23×C3×C5×C11×C16, …
maximal quotient ofC22×C3×C5×C11×C32, C2×C3×C4×C5×C11×C16, C23×C3×C5×C11×C16, …
automorphism group ofC17×C23×C31
outer automorphism group ofC17×C23×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.