Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C11⋊#14523572 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊#11760384 |
| commutator, hypocenter | C52×C7×C11 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C7×C11 | C2×C3 |
| prime radical | C2×C7×C11×C52⋊C3 | C2 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4620 |
Polycyclic presentation:
2,3,5^2,7,11,2|a^2=g,c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^10,c^b=cd,d^b=c^2d^3856 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 185);