Finite Group DatabasebetaFinite Group Databasebeta| order | 924 |
| isoclinism | isoclinic class of D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic77 |
| unambiguous semidirect product | C11⋊(C3×Dic7) |
| derived, Hall | C7×C11 ⋊ C3×C4 |
| Hall | C3×C7×C11 ⋊ C4 |
| Hall | C3×C11 ⋊ Dic7 |
| Hall | C3×C7 ⋊ Dic11 |
| Sylow | C11 ⋊ C3×Dic7 |
| Sylow | C7 ⋊ C3×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D77 |
| commutator, hypocenter | C7×C11 | C3×C4 |
| Frattini | C2 | C3×D77 |
| Fitting, socle, prime radical | C2×C3×C7×C11 | C2 |
| cosocle | C2×C7×C11 | C2×C3 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 924 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3)(4,5)(6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25);(4,6,5,7)(9,14)(10,13)(11,12)(16,25)(17,24)(18,23)(19,22)(20,21)240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D11×Dic7, C3×D7×Dic11, C3×#10597505, … |
| maximal normal subgroup of | C3×D11×Dic7, C3×D7×Dic11, C3×#10597505, … |
| maximal quotient of | C3×C7⋊(C11⋊C8), C2×C3×Dic77, C9×Dic77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(924, 7);