Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C213 |
| direct product | C2×C19×#2846 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
32890 conjugacy classes of subgroups; only the 1886 normal subgroups are shown.
This group has 32890 conjugacy classes of subgroups — too many to draw. Only its 1886 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(4,6)(8,10)(12,14);(7,8)(9,10);(11,12)(13,14);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29598);