Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#1043⋊ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C11⋊#1043)⋊ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C11 | C3×C4 |
| prime radical | C11×(C5⋊D5)⋊ΓL(1,𝔽8) | C2 |
| cosocle | C7×C11×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1155 |
Polycyclic presentation:
2,3,2,5^2,7,11|a^2=c,d^a=d^3,e^a=e^3,g^a=g^10,d^b=de^2,e^b=de^3,f^b=f^2,d^c=d^4,e^c=e^4224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 323);