Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C151 · Schur multiplier (H2) = C23 |
| direct product | C2×#352×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C151 | #99 |
| commutator | C23 | C22×C4×C151 |
| Frattini, cosocle | C2×D4 | C23×C151 |
| prime radical | C22×D4×C151 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C151 ◁ C23×C151 ◁ C22×D4×C151 ◁ G | |
278 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 169 |
| transitive degree | μt(G) = 4832 |
A minimal faithful permutation representation — 3 generators on 169 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(3,4)(5,11)(6,14,15,9)(7,10)(8,12,16,18)(13,17);(3,5,7,13)(4,8,10,16)(6,12,15,18)(9,11,14,17)3926 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#352×C151, C151×#12621, C151×#12688, … |
| maximal normal subgroup of | C4×#352×C151, C151×#12621, C151×#12688, … |
| maximal quotient of | C2×#1317×C151, C2×#1326×C151, C151×#11472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 851);