Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #3874⋊D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C11×C52⋊C3 | C22 |
| Fitting, socle | C52×C7×C11 | C2×D3 |
| LCS | G ▷ C7×C11×C52⋊C3 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 20 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:
2^2,3,7,11,5^2|c^a=c^2,d^a=d^6,e^a=e^10,f^a=fg,g^a=g^4,c^b=c^2,f^b=f^4g^4,f^c=g,g^c=f^4g^4508 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 288);