Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#551 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C47 |
| prime radical | #120×C47 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ G | |
248 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 150 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)(48,49,51,55)(50,56,57,53)(52,54,59,61)(58,62,63,60);(48,50,52,58)(49,53,54,60)(51,57,59,63)(55,56,61,62);(49,54)(53,60)(55,61)(56,62);(50,57)(53,56)(58,63)(60,62)1175 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#2197, C2×C47×#551, C47×#3475, … |
| maximal normal subgroup of | C47×#2197, C2×C47×#551, C47×#3475, … |
| maximal quotient of | C47×#2342, C47×#2343, C47×#2353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 232);