Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C210 |
| direct product | C22×#455×C67 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C22×H(5,𝔽2)×C67 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C23×C4×C67 ◁ G | |
5110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 87 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(3,4);(5,6,9,12)(7,13,15,20)(8,16,18,11)(10,17,19,14);(5,7)(6,10)(8,17)(9,15)(11,20)(12,19)(13,16)(14,18);(8,18)(11,16)(13,20)(14,17)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53367);