Finite Group DatabasebetaFinite Group Databasebeta| order | 496 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C31 ⋊ C2 |
| Sylow | C31 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D31 |
| commutator, socle, cosocle | C2×C31 | C23 |
| Fitting | Q8×C31 | C2 |
| hypercenter | Q8 | D31 |
| hypocenter | C31 | #41 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 248 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(32,34,35,38)(33,36,37,39);(32,33,35,37)(34,39,38,36);(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)(34,38)(36,39)Polycyclic presentation:
2^4,31|b^2=d,c^2=d,c^a=cd,e^a=e^30,c^b=cd85 conjugacy classes — view the full character table.
| maximal subgroup of | #11758491, #11758493, #11758495, … |
| maximal normal subgroup of | #11758491, #11758493, #11758495, … |
| maximal quotient of | #11758467, #11758469, #11758470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(496, 34);