Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C2×C4 |
| direct product | #1470×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C151 |
| Frattini, cosocle | C22×C4 | C23×C151 |
| prime radical | C23×C151 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G | |
204 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 3 generators on 183 points:
(1,2)(3,9,11,6)(4,7)(5,8)(10,15,16,13)(12,14)(17,18,20,23,21,24,27,30)(19,22,26,29,25,28,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183);(1,3,5,11)(2,6,8,9)(4,10,12,16)(7,13,14,15)(17,19)(18,22)(20,26)(21,25)(23,29)(24,28)(27,31)(30,32);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(19,25)(22,28)(26,31)(29,32)4832 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C151×#8476, C151×#8478, C151×#8485, … |
| maximal normal subgroup of | C151×#8476, C151×#8478, C151×#8485, … |
| maximal quotient of | C151×#7657, C151×#7660, C151×#7663, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 202);