Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C83×#2846 ⋊ C2 |
| Sylow | C83 ⋊ #36725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D83 |
| commutator, socle, cosocle | C23×C83 | C25 |
| Fitting | C83×#2846 | C2 |
| hypercenter | #2846 | D83 |
| hypocenter | C83 | #36725 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #2846 | |
3282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 2656 |
A minimal faithful permutation representation — 5 generators on 107 points:
(2,6)(5,7)(18,22)(21,24)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(2,6)(3,8)(19,23)(21,24);(10,14)(13,16)(19,23)(21,24);(1,3)(2,5)(4,8)(6,7)(9,11,12,15)(10,13,14,16)(17,19)(18,21)(20,23)(22,24)(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);(1,2)(3,7)(4,6)(5,8)(9,10)(11,13)(12,14)(15,16)(17,18)(19,21)(20,22)(23,24)Polycyclic presentation:
2^8,83|b^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^b=i^821856 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 376670);