Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊AGL(1,𝔽7))⋊D25 |
| unambiguous semidirect product | D275⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)⋊D25)⋊D11 |
| unambiguous semidirect product | (D77⋊D25)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C11×C25 | C22×C3 |
| Frattini | C5 | D55⋊AGL(1,𝔽7) |
| socle | C5×C7×C11 | C2×C3×D5 |
| LCS | G ▷ C7×C11×C25 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1925 |
Polycyclic presentation:
2^2,3,5,7,11,5|d^5=g^4,e^a=e^6,f^a=f^10,d^b=d^4g,e^b=e^6,g^b=g^4,e^c=e^2433 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 61);