Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C28 |
| direct product | C2×C53×#3240 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| prime radical | C2×#121×C53 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C22×C42×C53 ◁ G | |
1790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 5 generators on 87 points:
(1,2)(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);(3,4)(5,11)(6,9)(7,10)(8,13)(12,17)(14,16)(15,18)(19,20)(21,29)(22,28)(23,25)(24,27)(26,30)(31,34)(32,33);(3,5,7,13)(4,8,10,11)(6,14,15,12)(9,17,18,16)(20,25)(26,33)(27,28)(29,34);(3,6,7,15)(4,9,10,18)(5,12,13,14)(8,16,11,17)(19,21,23,31)(20,26,25,33)(22,30,24,32)(27,29,28,34);(4,10)(8,11)(9,18)(16,17)(19,22,23,24)(20,27,25,28)(21,30,31,32)(26,29,33,34)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53841);