Finite Group DatabasebetaFinite Group Databasebeta| order | 496 |
| isoclinism | isoclinic class of Dic62 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C31 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D31 |
| commutator, socle | C2×C31 | C2×C4 |
| Fitting | C2×C4×C31 | C2 |
| prime radical | C22×C31 | C4 |
| cosocle | C4×C31 | C22 |
| hypercenter | C2×C4 | D31 |
| hypocenter | C31 | M16 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 248 |
A minimal faithful permutation representation — 2 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)(33,36)(37,39);(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)(32,33,34,37,35,36,38,39)Polycyclic presentation:
2^4,31|a^2=c,c^2=d,b^a=bd,e^a=e^30130 conjugacy classes — view the full character table.
| maximal subgroup of | #11758393, #11758407, #11758410, … |
| maximal normal subgroup of | #11758393, #11758407, #11758410, … |
| maximal quotient of | #11758391, C4⋊(C31⋊C8), C22⋊(C31⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(496, 9);