Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C79 ⋊ #13812 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D79 |
| commutator | C22×C79 | C22×C42 |
| Fitting | C4×#95×C79 | C2 |
| socle, prime radical, cosocle | C24×C79 | C24 |
| hypercenter | C4×#95 | D79 |
| hypocenter | C79 | #13812 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
1546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(84,86,87,85)(90,95)(92,94);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(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)(89,93)(92,94)(96,98,99,103)(97,100,101,102);(80,81,82,83)(88,90)(89,92)(91,95)(93,94);(84,85,87,86)(88,89,91,93)(90,94,95,92)(96,97,99,101)(98,102,103,100)Polycyclic presentation:
2^8,79|a^2=g,b^2=h,c^2=ef,d^2=fg,b^a=be,c^a=cf,d^b=de,i^c=i^783220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 91056);