Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C53 · Schur multiplier (H2) = C27×C4 |
| direct product | C53×#60823 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C53 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C4×#41×C53 ◁ G | |
2054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,20)(12,18)(13,17)(14,16)(15,21)(19,26)(22,33)(23,27)(24,31)(25,30)(28,34)(29,35)(32,37)(36,38)(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);(1,3,4,8)(2,5,6,7)(9,11)(10,15)(12,22)(13,21)(14,23)(16,29)(17,20)(18,28)(19,27)(24,34)(25,36)(26,35)(30,39)(31,33)(32,38)(37,40);(3,8)(5,7)(10,16)(11,21)(14,26)(15,27)(17,19)(18,30)(20,29)(22,34)(25,37)(28,38)(31,32)(33,39);(2,6)(5,7)(10,17)(12,24)(15,20)(16,19)(22,34)(25,37)(27,29)(36,40);(9,12,13,24)(10,18,17,31)(11,22,21,34)(14,25,26,37)(15,28,20,33)(16,30,19,32)(23,36,35,40)(27,38,29,39)2756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 53811);