Finite Group DatabasebetaFinite Group Databasebeta| order | 24276 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11923883⋊ΓL(1,𝔽8) |
| Fitting, socle, derived, Hall | C7×C172 ⋊ C3×C4 |
| Hall | C7×#11923883 ⋊ C3 |
| Hall | C7⋊(C172⋊C3) ⋊ C4 |
| Hall | #11923883 ⋊ ΓL(1,𝔽8) |
| Sylow | C172 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #11923883⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C172 | C3×C4 |
| prime radical | (C17⋊D17)⋊ΓL(1,𝔽8) | C2 |
| cosocle | C7×C17⋊D17 | C2×C3 |
| LCS | G ▷ C7×C172 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 357 |
Polycyclic presentation:
2,3,2,7,17^2|a^2=c,e^a=e^4,f^a=f^4,d^b=d^2,e^b=e^12f^6,f^b=e^5f^4,e^c=e^16,f^c=f^16188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24276, 83);