Finite Group Databasebeta

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C23×C3×C4×C128 #72190643

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2818572288
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C4×C128
multiplicative(ℤ/53760)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C64C25×C3
socle, prime radicalC25×C3C2×C64
LCSG ▷ C1
UCSC1 ◁ G

11190 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C256, C23×C3×C8×C128, C22×C3×C42×C128, …
maximal normal subgroup ofC23×C3×C4×C256, C23×C3×C8×C128, C22×C3×C42×C128, …
maximal quotient ofC23×C3×C4×C256, C23×C3×C8×C128, C22×C3×C42×C128, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.