Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C26 |
| direct product | C2×C73×#2192 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×#131×C73 ◁ G | |
1150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(3,4)(5,16)(6,20)(7,14)(8,13)(9,15)(10,17)(11,18)(12,23)(19,31)(21,32)(22,26)(24,30)(25,29)(27,34)(28,33);(3,5)(4,10)(6,21)(7,18)(8,25)(9,19)(11,26)(12,29)(13,27)(14,32)(15,28)(16,20)(17,23)(22,33)(24,34)(30,31);(3,5)(4,11)(6,17)(7,25)(8,18)(9,19)(10,26)(12,28)(13,31)(14,16)(15,29)(20,32)(21,23)(22,34)(24,33)(27,30)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26522);