Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C25 |
| direct product | C2×C53×#1615 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C53 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C2×#121×C53 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C53 ◁ C23×C4×C53 ◁ G | |
1016 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 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);(3,4,7,10)(5,8,12,15)(6,9,13,16)(11,17,18,14)(19,20,24,27)(21,28,30,33)(22,26,23,31)(25,32,34,29);(3,5)(4,8)(6,11)(7,12)(9,14)(10,15)(13,18)(16,17)(19,21)(20,25)(22,29)(23,32)(24,30)(26,33)(27,34)(28,31);(3,6)(4,9)(5,11)(7,13)(8,14)(10,16)(12,18)(15,17)(19,22,24,23)(20,26,27,31)(21,29,30,32)(25,33,34,28)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 11094);