Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(ΓL(1,𝔽8)⋊#1043) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C11⋊#1043) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C11 | C3×C4 |
| prime radical | C11×ΓL(1,𝔽8)×C5⋊D5 | C2 |
| cosocle | C7×C11×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1925 |
Polycyclic presentation:
2,3,2,5^2,7,11|a^2=c,d^a=d^2,e^a=e^2,f^a=f^6,g^a=g^10,f^b=f^2,d^c=d^4,e^c=e^4394 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 358);