Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C71 · Schur multiplier (H2) = C28 |
| direct product | C71×#61292 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C71 |
| prime radical | #532×C71 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ #532×C71 ◁ G | |
1746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 5 generators on 111 points:
(1,2,5,4)(3,7,8,6)(9,10,14,18)(11,15,20,28)(12,17,23,32)(13,16,25,19)(21,27,33,38)(22,29,34,26)(24,30,36,31)(35,39,40,37)(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);(1,3)(2,6)(4,7)(5,8)(9,11)(10,15)(12,21)(13,22)(14,20)(16,29)(17,27)(18,28)(19,26)(23,33)(24,35)(25,34)(30,39)(31,37)(32,38)(36,40);(1,4,5,2)(3,7,8,6)(10,16)(11,20)(13,25)(15,26)(17,30)(18,19)(21,33)(24,36)(27,37)(28,29)(31,32)(38,39);(3,8)(6,7)(9,12)(10,17)(11,21)(13,24)(14,23)(15,27)(16,30)(18,32)(19,31)(20,33)(22,35)(25,36)(26,37)(28,38)(29,39)(34,40);(10,18)(11,20)(12,23)(16,19)(22,34)(24,36)(27,38)(37,39)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 54280);