Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C151 · Schur multiplier (H2) = C26 |
| direct product | C22×#101×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C151 | C22⋊C4 |
| commutator | C22 | C23×C4×C151 |
| Frattini, cosocle | C2×C4 | C24×C151 |
| prime radical | C24×C151 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G | |
736 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 9664 |
A minimal faithful permutation representation — 4 generators on 171 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(3,4);(5,6,8,12,9,11,17,19)(7,13,14,20,15,10,16,18);(5,7,9,15)(6,10,11,13)(8,16,17,14)(12,20,19,18)6644 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C151×#10741, C151×#10750, C151×#10763, … |
| maximal normal subgroup of | C151×#10741, C151×#10750, C151×#10763, … |
| maximal quotient of | C22×#324×C151, C2×#1461×C151, C2×#1463×C151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 1618);