Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#33360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C22×#99 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C2×D4 | C24×C61 |
| prime radical | C61×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×Q8×C61 ◁ C2×2−1+4×C61 ◁ G | |
1188 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,8)(4,9)(5,10,18,7)(6,11)(12,21)(13,22,28,19)(14,23)(15,24)(16,25,30,20)(17,26)(27,32,29,31)(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);(2,7)(5,18)(8,19)(9,20)(10,11)(13,28)(16,30)(21,31)(22,23)(24,32)(25,26)(27,29);(1,3,6,14)(2,8,11,23)(4,15,17,12)(5,13,18,28)(7,19,10,22)(9,24,26,21)(16,29,30,27)(20,32,25,31);(1,4,6,17)(2,9,11,26)(3,12,14,15)(5,16,18,30)(7,20,10,25)(8,21,23,24)(13,27,28,29)(19,31,22,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26348);