Finite Group DatabasebetaFinite Group Databasebeta| order | 3300 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×Dic33 |
| unambiguous semidirect product | C3⋊(C52×Dic11) |
| derived, Hall | C3×C11 ⋊ C4×C52 |
| Hall | C3×C52×C11 ⋊ C4 |
| Hall | C52×C11 ⋊ Dic3 |
| Hall | C3×C52 ⋊ Dic11 |
| Sylow | C11 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C52×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D33 |
| commutator, hypocenter | C3×C11 | C4×C52 |
| Frattini | C2 | C52×D33 |
| Fitting, socle, prime radical | C2×C3×C52×C11 | C2 |
| cosocle | C2×C3×C11 | C2×C52 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2×C52 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 3300 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4,5)(11,12)(13,14)(15,16,17)(18,19,20,21,22,23,24,25,26,27,28);(6,7,8,9,10)(11,13,12,14)(16,17)(19,28)(20,27)(21,26)(22,25)(23,24)900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic231, C52×C7×Dic33, C52×Dic363, … |
| maximal normal subgroup of | C52×C7×Dic33, C52×C11×Dic33 |
| maximal quotient of | C52×Dic231, C52×C7×Dic33, C52×Dic363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3300, 60);