Finite Group DatabasebetaFinite Group Databasebeta| order | 30592 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C239 · Schur multiplier (H2) = C28 |
| direct product | #3531×C239 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C239 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C239 |
| socle | C22×C239 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C239 ◁ G | |
930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 271 |
| transitive degree | μt(G) = 15296 |
A minimal faithful permutation representation — 5 generators on 271 points:
(1,2)(3,9)(4,8)(5,7)(6,10)(11,15)(12,14)(13,16)(17,18)(19,22)(20,27)(21,24)(23,29)(25,32)(26,31)(28,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271);(1,3)(2,6)(4,11)(5,10)(7,9)(8,13)(12,16)(14,15)(17,19,21,26)(18,22,24,31)(20,28,29,25)(23,32,27,30);(3,10)(6,9)(11,16)(13,15)(17,20,21,29)(18,23,24,27)(19,25,26,28)(22,30,31,32);(2,7)(3,10)(8,14)(11,16)(18,24)(22,31)(23,27)(30,32);(1,4,5,12)(2,8,7,14)(3,11,10,16)(6,13,9,15)9082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30592, 2263);