Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#20261660 |
| Fitting | C2×C16×C97 ⋊ C4 |
| Sylow | C97 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 3104 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,5,10,19,32,49,70,51,30,46,65,85,66,86,94,89,73,52,35,22,13,6,11,20,33,50,71,79,55,34,17,29,44,61,81,93,97,96,91,76,56,39,26,15,24,37,54,75,83,59,38,21,8,16,27,40,57,77,92,95,88,68,80,60,43,28,41,58,78,87,63,42,25,12,3,7,14,23,36,53,74,90,72,47,67,84,64,45,62,82,69,48,31,18,9,4)(100,101,102,105,103,107,108,112,104,106,109,111,110,113,115,114);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,81)(53,72,73,86)(57,70,76,82)(61,79,80,78)(65,83,84,75)(67,87,85,71)(74,88,89,93)(77,90,91,94)(92,95,96,97)(101,105,106,111)(102,108)(103,110)(107,114,113,112)(109,115);(98,99)800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 20855);