Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16×C71 · Schur multiplier (H2) = C4 |
| direct product | C71×#7329 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C16×C71 | C22 |
| commutator | C2 | C8×C16×C71 |
| Frattini, cosocle | C4×C16 | C22×C71 |
| socle, prime radical | C22×C71 | C4×C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C16×C71 ◁ G | |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 18176 |
A minimal faithful permutation representation — 2 generators on 111 points:
(9,10,11,16,12,17,19,28,13,18,20,29,22,30,31,38,14,15,21,25,23,26,32,35,24,27,33,36,34,37,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,2,3,5,4,6,7,8)(10,15)(16,25)(17,26)(18,27)(28,35)(29,36)(30,37)(38,40)11360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 317);