Finite Group DatabasebetaFinite Group Databasebeta| order | 19698 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C67 ⋊ C2×C3 |
| Hall | C67×#3862 ⋊ C2 |
| Hall | C7⋊D469 ⋊ C3 |
| Hall | #3862 ⋊ D67 |
| Sylow | C67 ⋊ #64425 |
| Sylow | C72 ⋊ C3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C67 | C2×C3 |
| LCS | G ▷ C72×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1407 |
A minimal faithful permutation representation — 2 generators on 81 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)(69,72,73,70,71,74)(76,80,79,77,78,81);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(68,69,71,74,73,72,70)(75,76,79,80,78,81,77)Polycyclic presentation:
2,3,7^2,67|c^a=c^6,d^a=d^6,e^a=e^66,c^b=c^2,d^b=d^4641 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19698, 47);