Finite Group DatabasebetaFinite Group Databasebeta| order | 2380 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C5×C17) |
| derived, Sylow | C7 ⋊ C4×C5×C17 |
| Hall | C5×C7×C17 ⋊ C4 |
| Hall | C7×C17 ⋊ C4×C5 |
| Hall | C5×C7 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C17 | D7 |
| commutator, hypocenter | C7 | C4×C5×C17 |
| Frattini | C2 | C5×D7×C17 |
| Fitting, socle, prime radical | C2×C5×C7×C17 | C2 |
| cosocle | C2×C7 | C2×C5×C17 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C5×C17 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 2380 |
A minimal faithful permutation representation — 2 generators on 33 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)(25,26)(27,28,29,30,31,32,33);(23,25,24,26)(28,33)(29,32)(30,31)850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×C25×Dic7, C52×C17×Dic7, C5×C17×Dic35, … |
| maximal normal subgroup of | C17×C25×Dic7, C52×C17×Dic7, C5×C7×C17×Dic7, … |
| maximal quotient of | C17×C25×Dic7, C52×C17×Dic7, C5×C17×Dic35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2380, 3);