Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C26 |
| direct product | C2×C53×#2192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C53 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ C2×#131×C53 ◁ G | |
1150 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)(5,14)(6,19)(7,24)(8,13)(9,15)(10,16)(11,22)(12,21)(17,29)(18,28)(20,25)(23,33)(26,31)(27,32)(30,34);(3,5)(4,9)(6,20)(7,16)(8,18)(10,11)(12,25)(13,27)(14,19)(15,22)(17,21)(23,31)(24,26)(28,33)(29,30)(32,34);(3,5)(4,10)(6,15)(7,17)(8,18)(9,11)(12,28)(13,29)(14,24)(16,21)(19,26)(20,22)(23,32)(25,33)(27,30)(31,34)2438 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26522);