Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C101 · Schur multiplier (H2) = C22 |
| direct product | C101×#1656 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C101 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C101 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C42×C101 ◁ G | |
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 117 points:
(2,5)(3,7)(6,8)(10,13)(11,15)(14,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117);(1,2,4,6)(3,8,7,5)(11,15)(13,16);(3,7)(5,8)(9,10)(11,16)(12,14)(13,15)2020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#7523, C2×C101×#1656, C101×#18984, … |
| maximal normal subgroup of | C101×#7523, C2×C101×#1656, C101×#18984, … |
| maximal quotient of | C101×#7735, C101×#7737, C101×#7746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 388);