Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C53×#18470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#3560 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C2×C42×C53 ◁ G | |
906 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(3,10)(4,6)(5,9)(7,11)(8,13)(12,15)(14,16)(17,18,22,26)(19,23,29,36)(20,24,31,38)(21,32,33,25)(27,39,41,34)(28,42,43,35)(30,44,45,37)(40,46,48,47)(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);(2,6)(4,13)(7,14)(8,9)(10,15)(12,16)(17,19)(18,23)(20,27)(21,28)(22,29)(24,34)(25,35)(26,36)(30,40)(31,41)(32,42)(33,43)(37,46)(38,39)(44,47)(45,48);(3,11)(7,10)(12,16)(14,15)(17,20)(18,24)(19,27)(21,30)(22,31)(23,34)(25,37)(26,38)(28,40)(29,41)(32,44)(33,45)(35,46)(36,39)(42,47)(43,48);(1,3,5,11)(2,7,9,10)(4,12,13,16)(6,14,8,15)(17,21,22,33)(18,25,26,32)(19,28,29,43)(20,30,31,45)(23,35,36,42)(24,37,38,44)(27,40,41,48)(34,46,39,47)1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11458);