Finite Group DatabasebetaFinite Group Databasebeta| order | 4672 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C73 · Schur multiplier (H2) = C1 |
| direct product | M64×C73 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C73 | C22 |
| commutator | C2 | C2×C16×C73 |
| Frattini, cosocle | C16 | C22×C73 |
| socle | C2×C73 | C2×C16 |
| prime radical | C22×C73 | C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C73 ◁ G | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 105 |
| transitive degree | μt(G) = 2336 |
A minimal faithful permutation representation — 2 generators on 105 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(2,18)(4,20)(6,22)(8,24)(10,26)(12,28)(14,30)(16,32)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4672, 51);