Finite Group DatabasebetaFinite Group Databasebeta| order | 496 |
| isoclinism | isoclinic class of #92479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C31 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D31 |
| commutator, cosocle | C4×C31 | C22 |
| Frattini | C4 | C2×D31 |
| Fitting | Q8×C31 | C2 |
| socle, prime radical | C2×C31 | D4 |
| hypercenter | Q8 | D31 |
| hypocenter | C31 | Q16 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
A minimal faithful permutation representation — 2 generators on 47 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)(32,34,36,42)(33,37,39,46)(35,44,45,41)(38,47,43,40);(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)(32,33,36,39)(34,40,42,47)(35,43,45,38)(37,44,46,41)Polycyclic presentation:
2^4,31|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^30,c^b=cd82 conjugacy classes — view the full character table.
| maximal subgroup of | #11758492, #11758493, Q16×D31, … |
| maximal normal subgroup of | #11758492, #11758493, Q16×D31, … |
| maximal quotient of | #11758395, #11758398, #11758423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(496, 17);