Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C103 ⋊ #2295 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D103 |
| commutator | C22×C103 | C23×C4 |
| Fitting | #389×C103 | C2 |
| socle, prime radical, cosocle | C23×C103 | C24 |
| hypercenter | #389 | D103 |
| hypocenter | C103 | #2295 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ #389 | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 4 generators on 123 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(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)(116,118,119,122)(117,121,120,123);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(108,110,111,115)(109,112,113,114);(104,106,107,105)(117,120)(121,123);(104,105,107,106)(108,109,111,113)(110,114,115,112)(116,117)(118,121)(119,120)(122,123)Polycyclic presentation:
2^7,103|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^d=h^1021484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 6981);