Finite Group DatabasebetaFinite Group Databasebeta| order | 496 |
| isoclinism | isoclinic class of Dic62 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C31 ⋊ C2 |
| Sylow | C31 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D31 |
| commutator, socle, cosocle | C2×C31 | C23 |
| Frattini | C2 | C22×D31 |
| Fitting | C2×C4×C31 | C2 |
| hypercenter | C2×C4 | D31 |
| hypocenter | C31 | #41 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
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)(33,37)(36,39);(32,34,35,38)(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)(34,36)(35,37)(38,39)Polycyclic presentation:
2^4,31|b^2=d,c^a=cd,e^a=e^30130 conjugacy classes — view the full character table.
| maximal subgroup of | #11758393, #11758413, #11758478, … |
| maximal normal subgroup of | #11758393, #11758413, #11758478, … |
| maximal quotient of | C4×Dic62, #11758447, #11758449, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(496, 30);