Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| unambiguous semidirect product | D7⋊(C11⋊((C5⋊D5)⋊C3)) |
| unambiguous semidirect product | (D7⋊(C52⋊C3))⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C11 | C22×C3 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1155 |
Polycyclic presentation:
2^2,3,5^2,7,11|d^a=d^4,e^a=e^4,g^a=g^10,f^b=f^6,d^c=de,e^c=d^2e^3,f^c=f^2269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 309);