Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C233 · Schur multiplier (H2) = C25 |
| direct product | #575×C233 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C233 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C24×C233 |
| socle | C2×C233 | C22×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C233 ◁ C22×C4×C233 ◁ G | |
262 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 249 |
| transitive degree | μt(G) = 3728 |
A minimal faithful permutation representation — 4 generators on 249 points:
(1,2)(3,10)(4,9)(5,13)(6,8)(7,11)(12,16)(14,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249);(1,3)(2,7)(4,11)(5,14)(6,12)(8,15)(9,16)(10,13);(2,8)(7,15)(9,13)(10,16);(1,4,6,5)(2,9,8,13)(3,11,12,14)(7,16,15,10)5126 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1881×C233, #1906×C233, #2008×C233, … |
| maximal normal subgroup of | #1881×C233, #1906×C233, #2008×C233, … |
| maximal quotient of | #2896×C233, #2911×C233, #2943×C233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 256);