Finite Group DatabasebetaFinite Group Databasebeta| order | 19328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C151 · Schur multiplier (H2) = C2 |
| direct product | #2239×C151 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C151 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C151 |
| prime radical | C23×C151 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×M16×C151 ◁ G | |
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 4832 |
A minimal faithful permutation representation — 3 generators on 183 points:
(1,2,6,10)(3,11,12,29)(4,15,16,32)(5,20,18,9)(7,22,23,13)(8,25,26,19)(14,27,21,30)(17,24,31,28)(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);(4,16)(8,26)(11,29)(13,22)(15,32)(17,31)(19,25)(27,30);(1,3,5,21,6,12,18,14)(2,7,9,28,10,23,20,24)(4,17,19,22,16,31,25,13)(8,27,15,29,26,30,32,11)3020 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C151×#12299, C151×#12300, C151×#12302, … |
| maximal normal subgroup of | C151×#12299, C151×#12300, C151×#12302, … |
| maximal quotient of | C151×#12875, C151×#12931, C151×#13009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19328, 971);