Finite Group DatabasebetaFinite Group Databasebeta| order | 24448 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C191 · Schur multiplier (H2) = C25 |
| direct product | #1791×C191 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C191 | #120 |
| commutator | C23 | C22×C4×C191 |
| Frattini, cosocle | C22×C4 | C23×C191 |
| socle | C2×C191 | #379 |
| prime radical | #585×C191 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C191 ◁ C22×C4×C191 ◁ G | |
548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 223 |
| transitive degree | μt(G) = 6112 |
A minimal faithful permutation representation — 3 generators on 223 points:
(1,2,5,10,6,9,18,23)(3,11,14,24,13,7,17,20)(4,8,16,21,15,22,28,32)(12,19,27,30,26,25,29,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223);(1,3)(2,7)(4,12)(5,17)(6,13)(8,19)(9,11)(10,24)(14,18)(15,26)(16,29)(20,23)(21,31)(22,25)(27,28)(30,32);(1,4)(2,8)(3,12)(5,16)(6,15)(7,19)(9,22)(10,21)(11,25)(13,26)(14,27)(17,29)(18,28)(20,30)(23,32)(24,31)6112 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24448, 523);