Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60388 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C210 |
| direct product | C53×#60391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C53 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C53 ◁ C2×#41×C53 ◁ G | |
4666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 5 generators on 85 points:
(1,2,7,11)(3,12,16,26)(4,5,9,19)(6,20,22,10)(8,21,24,15)(13,27,23,32)(14,28,30,29)(17,31,25,18)(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);(1,3)(2,8)(4,13)(5,14)(6,21)(7,16)(9,23)(10,26)(11,24)(12,20)(15,22)(17,28)(18,32)(19,30)(25,29)(27,31);(1,2,7,11)(3,8,16,24)(4,5,9,19)(6,20,22,10)(12,15,26,21)(13,14,23,30)(17,31,25,18)(27,29,32,28);(1,4)(2,5)(3,13)(6,17)(7,9)(8,14)(10,18)(11,19)(12,27)(15,29)(16,23)(20,31)(21,28)(22,25)(24,30)(26,32);(1,5)(2,9)(3,14)(4,11)(6,18)(7,19)(8,23)(10,25)(12,28)(13,24)(15,27)(16,30)(17,20)(21,32)(22,31)(26,29)3074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53379);