Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11126 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #390 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25)(26,36)(27,41,45,32)(28,35)(29,33)(30,34)(31,38)(37,52,54,49)(39,47)(40,48)(42,55,53,46)(43,50,44,51);(20,21,22,23)(24,26,28,38,30,40,29,39)(25,31,33,36,34,47,35,48)(27,42,43,37,45,53,44,54)(32,49,50,46,41,52,51,55);(24,27)(25,32)(26,37)(28,44)(29,43)(30,45)(31,46)(33,51)(34,41)(35,50)(36,49)(38,42)(39,53)(40,54)(47,55)(48,52)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4114);