Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C22 |
| direct product | C47×#468 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C47 |
| prime radical | #121×C47 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G | |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49)(50,51)(53,56)(54,58)(57,59);(52,53,54,56,55,57,58,59);(49,51)(53,57)(56,59)752 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C47×#468, C47×#3054, C47×#3055, … |
| maximal normal subgroup of | C2×C47×#468, C47×#3054, C47×#3055, … |
| maximal quotient of | C47×#1685, C47×#1686, C47×#1691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 149);