Finite Group DatabasebetaFinite Group Databasebeta| order | 464 |
| isoclinism | isoclinic class of #90782 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C29 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D29 |
| commutator, cosocle | C4×C29 | C22 |
| Frattini | C4 | C2×D29 |
| Fitting | Q8×C29 | C2 |
| socle, prime radical | C2×C29 | D4 |
| hypercenter | Q8 | D29 |
| hypocenter | C29 | Q16 |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 464 |
A minimal faithful permutation representation — 2 generators on 45 points:
(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)(30,32,34,40)(31,35,37,44)(33,42,43,39)(36,45,41,38);(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)(30,31,34,37)(32,38,40,45)(33,41,43,36)(35,42,44,39)Polycyclic presentation:
2^4,29|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^28,c^b=cd77 conjugacy classes — view the full character table.
| maximal subgroup of | #11745277, #11745278, Q16×D29, … |
| maximal normal subgroup of | #11745277, #11745278, Q16×D29, … |
| maximal quotient of | #11745155, #11745158, #11745183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(464, 18);