Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C7⋊(C11⋊#64480) |
| unambiguous semidirect product | C11⋊(C7⋊#64480) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C7×C11×C52⋊C3 | C4 |
| Fitting, socle | C52×C7×C11 | Dic3 |
| prime radical, cosocle | C7×C11×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C7×C11×C52⋊C3 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1155 |
Polycyclic presentation:
2^2,3,7,11,5^2|a^2=b,c^a=c^2,d^a=d^6,e^a=e^10,f^a=fg^2,g^a=f^4g^4,f^b=f^4,g^b=g^4,f^c=f^2g^4,g^c=f^2g^2388 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 297);