Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C47 · Schur multiplier (H2) = C25 |
| direct product | C47×#575 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C47 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C24×C47 |
| socle | C2×C47 | C22×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C47 ◁ C22×C4×C47 ◁ G | |
262 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 752 |
A minimal faithful permutation representation — 4 generators on 63 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49)(50,57)(51,56)(52,60)(53,55)(54,58)(59,63)(61,62);(48,50)(49,54)(51,58)(52,61)(53,59)(55,62)(56,63)(57,60);(49,55)(54,62)(56,60)(57,63);(48,51,53,52)(49,56,55,60)(50,58,59,61)(54,63,62,57)1034 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#1881, C47×#1906, C47×#2008, … |
| maximal normal subgroup of | C47×#1881, C47×#1906, C47×#2008, … |
| maximal quotient of | C47×#2896, C47×#2911, C47×#2943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 256);