Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #3874⋊D17 |
| Fitting, socle, Hall | C52×C17 ⋊ C2×D3 |
| derived, Hall | C17×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ C2×D17 |
| Sylow | C52 ⋊ D3×D17 |
| Sylow | C17 ⋊ #3874⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C17×C52⋊C3 | C22 |
| Fitting, socle | C52×C17 | C2×D3 |
| LCS | G ▷ C17×C52⋊C3 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,5^2|c^a=c^2,d^a=d^16,e^a=ef,f^a=f^4,c^b=c^2,e^b=e^4f^4,e^c=f,f^c=e^4f^4118 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#3874⋊D17, #3874⋊D51, #29505887, … |
| maximal normal subgroup of | C3×#3874⋊D17, C7×#3874⋊D17 |
| maximal quotient of | #90646⋊D17, C3×#3874⋊D17, #3874⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 57);