Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C11⋊#64470) |
| unambiguous semidirect product | C11⋊(C7⋊#64470) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C11⋊#3874) |
| commutator, hypocenter | C7×C11×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C7×C11 | D3 |
| prime radical, cosocle | C2×C7×C11×C52⋊C3 | C2 |
| LCS | G ▷ C7×C11×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4620 |
Polycyclic presentation:
2,3,7,11,5^2,2|a^2=g,b^a=b^2,c^a=c^6,d^a=d^10,e^a=e^2f^4,f^a=e^3f^3,e^b=e^2f^4,f^b=e^2f^2862 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 177);