Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#12685 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #120 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1779 |
| prime radical | C19×#585 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C22×C8×C19 ◁ G | |
890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,31,26,32,46,59,27,33,47,60,24,30,44,57)(22,34,38,62,36,50,68,58,37,55,45,73,42,28,48,51)(23,29,40,53,39,52,69,78,41,54,71,80,43,56,72,81)(35,63,66,83,67,49,75,77,65,61,70,82,64,76,74,79);(20,22)(21,28)(23,35)(24,42)(25,45)(26,36)(27,37)(29,49)(30,55)(31,58)(32,34)(33,50)(38,47)(39,67)(40,70)(41,65)(43,64)(44,68)(46,48)(51,60)(52,61)(53,79)(54,76)(56,63)(57,62)(59,73)(66,71)(69,74)(72,75)(77,80)(78,83)(81,82);(20,23)(21,29)(22,35)(24,43)(25,40)(26,39)(27,41)(28,49)(30,56)(31,53)(32,52)(33,54)(34,61)(36,67)(37,65)(38,66)(42,64)(44,72)(45,70)(46,69)(47,71)(48,74)(50,76)(51,77)(55,63)(57,81)(58,79)(59,78)(60,80)(62,82)(68,75)(73,83)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5673);