Finite Group DatabasebetaFinite Group Databasebeta| order | 24612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊#11924078) |
| unambiguous semidirect product | C7⋊(C3⋊#11924078) |
| Fitting, socle, derived, Hall | C3×C7×C293 ⋊ C4 |
| Hall | C7×C293 ⋊ Dic3 |
| Hall | C3×C293 ⋊ Dic7 |
| Sylow | C293 ⋊ Dic21 |
| Hall | C3×C7 ⋊ #11924078 |
| Sylow | C7 ⋊ C3⋊#11924078 |
| Sylow | C3 ⋊ C7⋊#11924078 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C293 | C4 |
| prime radical, cosocle | C3×C7×D293 | C2 |
| LCS | G ▷ C3×C7×C293 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6153 |
Polycyclic presentation:
2^2,3,7,293|a^2=b,c^a=c^2,d^a=d^6,e^a=e^138,e^b=e^2921557 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24612, 25);