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×#33371 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C22×#99 |
| commutator | C2×C4 | C23×C4×C61 |
| Frattini, cosocle | C2×Q8 | C24×C61 |
| prime radical | C61×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×Q8×C61 ◁ C2×H(5,𝔽2)×C61 ◁ G | |
1208 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2,7,12,8,13,4,10)(3,14,15,30,17,25,22,32)(5,11,19,29,6,20,18,28)(9,23,26,21,27,31,24,16)(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);(1,3)(2,9)(4,15)(5,16)(6,21)(7,22)(8,17)(10,24)(11,25)(12,26)(13,27)(14,20)(18,23)(19,31)(28,30)(29,32);(1,4,8,7)(2,10,13,12)(3,15,17,22)(5,19,6,18)(9,24,27,26)(11,29,20,28)(14,30,25,32)(16,31,21,23);(1,5,8,6)(2,11,13,20)(3,16,17,21)(4,18,7,19)(9,25,27,14)(10,28,12,29)(15,23,22,31)(24,30,26,32)2806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26359);