Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C27 |
| direct product | C71×#23874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C22×C4×C71 ◁ G | |
1674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,8)(4,15)(5,7)(6,11)(9,16)(10,18)(12,27)(13,22)(14,24)(17,26)(19,21)(20,25)(23,28)(29,31)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(2,7)(5,18)(8,22)(9,15)(10,11)(13,19)(16,20)(21,24)(23,27)(25,26)(28,30)(31,32);(1,3,6,14)(2,8,11,24)(4,12,17,29)(5,19,18,13)(7,21,10,22)(9,23,25,32)(15,31,26,27)(16,30,20,28);(1,4)(2,9)(3,12)(5,20)(6,17)(7,15)(8,23)(10,26)(11,25)(13,30)(14,29)(16,18)(19,28)(21,31)(22,27)(24,32)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16862);