Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C22 |
| direct product | C4×SD16×C47 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | D4 |
| commutator | C4 | C22×C4×C47 |
| Frattini, cosocle | C2×C4 | C23×C47 |
| socle | C22×C47 | C2×D4 |
| prime radical | C2×D4×C47 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C42×C47 ◁ G | |
122 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(5,6,7,8,9,10,11,12);(6,8)(7,11)(10,12)1316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×SD16×C47, C47×SD16⋊C8, C47×#1582, … |
| maximal normal subgroup of | C8×SD16×C47, C47×SD16⋊C8, C47×#1582, … |
| maximal quotient of | C8×SD16×C47, C47×#1582, C47×#1583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 119);