Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#16812392 |
| derived, Hall | C7×C172⋊C3 ⋊ C4 |
| Hall | C7×C172 ⋊ Dic3 |
| Hall | C172⋊C3 ⋊ Dic7 |
| Sylow | C172 ⋊ Dic21 |
| Sylow | C7 ⋊ #16812392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊#13181892 |
| commutator, hypocenter | C7×C172⋊C3 | C4 |
| Fitting, socle | C2×C7×C172 | D3 |
| prime radical, cosocle | C2×C7×C172⋊C3 | C2 |
| LCS | G ▷ C7×C172⋊C3 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1428 |
Polycyclic presentation:
2,3,7,17^2,2|a^2=f,b^a=b^2,c^a=c^6,e^a=de^16,d^b=d^2e^12,e^b=d^15e^14744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 52);