Finite Group DatabasebetaFinite Group Databasebeta| order | 24108 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #22548819⋊C3 |
| Fitting, socle, derived, Hall | C72×C41 ⋊ C3×C4 |
| Hall | #22548819 ⋊ C3 |
| Hall | C41×#3861 ⋊ C4 |
| Hall | #3861 ⋊ Dic41 |
| Sylow | C72 ⋊ C3×Dic41 |
| Sylow | C41 ⋊ #5997⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C41 | C3×C4 |
| prime radical | C41×#64424 | C2 |
| cosocle | C41×C7⋊D7 | C2×C3 |
| LCS | G ▷ C72×C41 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 574 |
Polycyclic presentation:
2,3,2,7^2,41|a^2=c,d^a=d^5e^3,e^a=d^3e^2,f^a=f^40,d^b=d^4,e^b=e^4,d^c=d^6,e^c=e^6296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24108, 86);