Finite Group DatabasebetaFinite Group Databasebeta| order | 2380 |
| isoclinism | isoclinic class of D595 |
| automorphism | Aut(G) order 456960 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D1190 |
| direct product | C2×D595 |
| unambiguous semidirect product | (C2×C5)⋊D119 |
| unambiguous semidirect product | (C2×C7)⋊D85 |
| unambiguous semidirect product | (C2×C17)⋊D35 |
| Fitting, socle | C2×C5×C7×C17 ⋊ C2 |
| derived, Hall | C5×C7×C17 ⋊ C22 |
| Hall | C7×C17 ⋊ C2×D5 |
| Hall | C5×C17 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D35 |
| Sylow | C7 ⋊ C2×D85 |
| Sylow | C5 ⋊ C2×D119 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D595 |
| commutator, cosocle, hypocenter | C5×C7×C17 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C17 | C2 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1190 |
A minimal faithful permutation representation — 2 generators on 31 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);(4,7)(5,6)(9,14)(10,13)(11,12)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D2975, D5×D595, C2×C5⋊D595, … |
| maximal normal subgroup of | C2×C5×D595, C2×C7×D595, C2×C11×D595, … |
| maximal quotient of | C2×D2975, D5×D595, C2×C5⋊D595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2380, 29);