Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#9416 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #386 |
| commutator | C42 | C22×C4×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| prime radical | C23×C53 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
380 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 3 generators on 101 points:
(1,2)(3,11,14,15)(4,8,7,13)(5,9)(6,10)(12,16)(17,18)(19,23,28,38)(20,30)(21,33)(22,25)(24,31)(26,35)(27,41,42,48)(29,45,44,37)(32,40)(34,39)(36,46,47,43)(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);(1,3,5,8,6,14,16,13)(2,7,9,15,10,4,12,11)(17,19)(18,23,25,38)(20,27)(21,29)(22,28)(24,36,39,47)(26,37,33,45)(30,41,40,48)(31,43)(32,42)(34,46)(35,44);(1,4)(2,8)(3,12)(5,11)(6,7)(9,14)(10,13)(15,16)(17,20,22,32)(18,24,25,39)(19,27,28,42)(21,34,35,31)(23,36,38,47)(26,40,33,30)(29,46,44,43)(37,48,45,41)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 2404);