Finite Group Databasebeta

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C3×C4×C7×C128 #72189290

order10752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 24576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C7×C128
multiplicative(ℤ/13445)ˣ, (ℤ/26890)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C64C22×C3×C7
socle, prime radicalC22×C3×C7C2×C64
LCSG ▷ C1
UCSC1 ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C7×C256, C3×C7×C8×C128, C2×C3×C4×C7×C128, …
maximal normal subgroup ofC3×C4×C7×C256, C3×C7×C8×C128, C2×C3×C4×C7×C128, …
maximal quotient ofC3×C4×C7×C256, C3×C7×C8×C128, C2×C3×C4×C7×C128, …
automorphism group ofC5×C2689
outer automorphism group ofC5×C2689

GAP

Past the SmallGroups library coverage — no SmallGroups id.