Finite Group DatabasebetaFinite Group Databasebeta| order | 464 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C29 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D29 |
| commutator, hypocenter | C29 | C16 |
| Fitting, cosocle | C8×C29 | C2 |
| socle, prime radical | C2×C29 | C8 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
A minimal faithful permutation representation — 2 generators on 45 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)(30,31,32,35,33,36,38,41,34,37,39,42,40,43,44,45);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)Polycyclic presentation:
2^4,29|a^2=b,b^2=c,c^2=d,e^a=e^28128 conjugacy classes — view the full character table.
| maximal subgroup of | #11745144, C16×D29, #11745146, … |
| maximal normal subgroup of | #11745144, C16×D29, #11745146, … |
| maximal quotient of | #11745142, C2×#90768, C3×#90768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(464, 1);