Finite Group DatabasebetaFinite Group Databasebeta| order | 24108 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C3⋊(C7⋊(C7⋊#4223)) |
| unambiguous semidirect product | C7⋊(C3⋊(C7⋊#4223)) |
| Fitting, socle, derived, Hall | C3×C72×C41 ⋊ C4 |
| Hall | C72×C41 ⋊ Dic3 |
| Hall | C3×C72 ⋊ #4223 |
| Hall | C3×C41 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C3⋊#4223 |
| Sylow | C41 ⋊ C3⋊(C7⋊Dic7) |
| Sylow | C3 ⋊ C7⋊(C7⋊#4223) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C41 | C4 |
| prime radical, cosocle | C3×C72×D41 | C2 |
| LCS | G ▷ C3×C72×C41 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6027 |
Polycyclic presentation:
2^2,3,7^2,41|a^2=b,c^a=c^2,d^a=d^6,e^a=e^6,f^a=f^32,f^b=f^401620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24108, 162);