Finite Group DatabasebetaFinite Group Databasebeta| order | 464 |
| isoclinism | isoclinic class of #90796 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C29 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#1181 |
| commutator, socle | C2×C29 | C2×C4 |
| Fitting | C4×C29 | C4 |
| prime radical | C2×D29 | C4 |
| cosocle | Dic29 | C22 |
| hypercenter | C4 | #1181 |
| hypocenter | C29 | M16 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 232 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,5,10,19,15,23,17,26,28,24,12,3,7,14,22,13,6,11,20,27,29,25,21,8,16,18,9,4)(30,32,34,33)(31,35,36,37);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,25)(14,21,22,23)(16,24,19,20)(26,28,29,27)(30,31,33,35,34,36,32,37)Polycyclic presentation:
2^4,29|a^2=c,b^2=d,c^2=d,b^a=bd,e^a=e^12,e^c=e^2838 conjugacy classes — view the full character table.
| maximal subgroup of | #11745211, #11745212, #11745224, … |
| maximal normal subgroup of | #11745211, #11745212, #11745224, … |
| maximal quotient of | C4⋊#6599, #11745218, #11745219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(464, 29);