Finite Group Databasebeta

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C2×C3×C42×C9×C16 #72192028

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1358954496
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3×C43

Aliases

abelianC2×C3×C42×C9×C16
multiplicative(ℤ/20995)ˣ, (ℤ/22015)ˣ, (ℤ/24531)ˣ, (ℤ/28305)ˣ, (ℤ/29835)ˣ, (ℤ/30784)ˣ, (ℤ/32708)ˣ, (ℤ/41990)ˣ, (ℤ/44030)ˣ, (ℤ/49062)ˣ, (ℤ/56610)ˣ, (ℤ/59670)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3×C8C24×C32
socle, prime radicalC24×C32C22×C3×C8
LCSG ▷ C1
UCSC1 ◁ G

14100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C42×C9×C32, C2×C3×C4×C8×C9×C16, C3×C43×C9×C16, …
maximal normal subgroup ofC2×C3×C42×C9×C32, C2×C3×C4×C8×C9×C16, C3×C43×C9×C16, …
maximal quotient ofC2×C3×C42×C9×C32, C2×C3×C4×C8×C9×C16, C3×C43×C9×C16, …
automorphism group ofC5×C13×C17×C27, C13×C37×C64
outer automorphism group ofC5×C13×C17×C27, C13×C37×C64

GAP

Past the SmallGroups library coverage — no SmallGroups id.