Finite Group DatabasebetaFinite Group Databasebeta| order | 24832 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C97 · Schur multiplier (H2) = C2 |
| direct product | C97×#7065 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C97 | #99 |
| commutator | C22×C4 | C2×C8×C97 |
| Frattini, cosocle | C2×C4⋊C8 | C22×C97 |
| socle | C22×C97 | #324 |
| prime radical | C23×C97 | C22⋊C8 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C97 ◁ C22×C4×C97 ◁ C2×C4⋊C8×C97 ◁ G | |
156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 2 generators on 145 points:
(1,2)(3,9,11,15)(4,12,13,7)(5,8)(6,10)(14,16)(17,18,20,25,21,26,31,39,22,24,30,36,32,37,43,46)(19,23,28,33,29,35,42,44,27,34,40,38,41,45,48,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(1,3)(2,6,8,14)(4,10)(5,11)(7,9,12,15)(13,16)(17,19)(18,23,24,34)(20,28)(21,29)(22,27)(25,38,36,33)(26,35,37,45)(30,40)(31,42)(32,41)(39,47,46,44)(43,48)4462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24832, 53);