Finite Group Databasebeta

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C2×C3×C4×C9×C64 #72191998

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1769472
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C3×C4×C9×C64
multiplicative(ℤ/18335)ˣ, (ℤ/20195)ˣ, (ℤ/21423)ˣ, (ℤ/22503)ˣ, (ℤ/25965)ˣ, (ℤ/26055)ˣ, (ℤ/28564)ˣ, (ℤ/30004)ˣ, (ℤ/36670)ˣ, (ℤ/40390)ˣ, (ℤ/42846)ˣ, (ℤ/45006)ˣ, (ℤ/51930)ˣ, (ℤ/52110)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C32C23×C32
socle, prime radicalC23×C32C2×C3×C32
LCSG ▷ C1
UCSC1 ◁ G

1620 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×C4×C9×C128, C2×C3×C8×C9×C64, C3×C42×C9×C64, …
maximal normal subgroup ofC2×C3×C4×C9×C128, C2×C3×C8×C9×C64, C3×C42×C9×C64, …
maximal quotient ofC2×C3×C4×C9×C128, C2×C3×C8×C9×C64, C3×C42×C9×C64, …
automorphism group ofC5×C19×C193, C5×C27×C193
outer automorphism group ofC5×C19×C193, C5×C27×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.