Finite Group DatabasebetaFinite Group Databasebeta| order | 64260 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D32130 |
| direct product | C2×D16065 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D16065 |
| commutator, cosocle, hypocenter | C5×C7×C17×C27 | C22 |
| Frattini | C9 | C2×D1785 |
| Fitting | C2×C5×C7×C17×C27 | C2 |
| socle | C2×C3×C5×C7×C17 | D9 |
| LCS | G ▷ C5×C7×C17×C27 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 32130 |
A minimal faithful permutation representation — 2 generators on 58 points:
(1,2)(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);(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,34)(32,33)(36,41)(37,40)(38,39)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)16068 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2)(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), (4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,34)(32,33)(36,41)(37,40)(38,39)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51));