Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C17 |
| unambiguous semidirect product | D7⋊((C17⋊D17)⋊C3) |
| unambiguous semidirect product | #27131466⋊C2 |
| unambiguous semidirect product | (D7⋊(C172⋊C3))⋊C2 |
| unambiguous semidirect product | ((C17⋊D17)⋊ΓL(1,𝔽8))⋊C2 |
| Fitting, socle, derived, Hall | C7×C172 ⋊ C22×C3 |
| Hall | D7×C17⋊D17 ⋊ C3 |
| Hall | C7⋊(C172⋊C3) ⋊ C22 |
| Sylow | C172 ⋊ C2×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C2×(C17⋊D17)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C172 | C22×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 357 |
Polycyclic presentation:
2^2,3,7,17^2|e^a=e^16,f^a=f^16,d^b=d^6,d^c=d^2,e^c=e^12f^6,f^c=e^5f^4254 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 73);