Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D21⋊(D11⋊C25) |
| unambiguous semidirect product | (D21⋊D11)⋊C25 |
| unambiguous semidirect product | (C3⋊(D11⋊C25))⋊D7 |
| unambiguous semidirect product | (C7⋊(D11⋊C25))⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D21⋊AGL(1,𝔽11) |
| commutator, hypocenter | C3×C7×C11 | C22×C25 |
| Fitting, socle, cosocle | C3×C5×C7×C11 | C22×C5 |
| prime radical | C5×D21⋊D11 | C5 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5775 |
Polycyclic presentation:
2^2,5,3,7,11,5|c^5=g,e^a=e^6,f^a=f^10,d^b=d^2,e^b=e^6,f^c=f^4435 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 47);