Finite Group Databasebeta

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C22×C3×C9×C128 #72191992

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 663552
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C9×C128
multiplicative(ℤ/24213)ˣ, (ℤ/32284)ˣ, (ℤ/41508)ˣ, (ℤ/48426)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C64C23×C32
socle, prime radicalC23×C32C3×C64
LCSG ▷ C1
UCSC1 ◁ G

820 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 ofC22×C3×C9×C256, C2×C3×C4×C9×C128, C23×C3×C9×C128
maximal normal subgroup ofC22×C3×C9×C256, C2×C3×C4×C9×C128, C23×C3×C9×C128
maximal quotient ofC22×C3×C9×C256, C2×C3×C4×C9×C128, C23×C3×C9×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.