Finite Group DatabasebetaFinite Group Databasebeta| order | 464 |
| isoclinism | isoclinic class of #90782 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C29 ⋊ C2 |
| Sylow | C29 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D29 |
| commutator, cosocle | C4×C29 | C22 |
| Frattini | C4 | C2×D29 |
| Fitting | D4×C29 | C2 |
| socle | C2×C29 | D4 |
| hypercenter | D4 | D29 |
| hypocenter | C29 | D8 |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 232 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(31,34)(32,37)(35,36);(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)(32,34)(33,36)(35,37)Polycyclic presentation:
2^4,29|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 | D8×D29, #11745273, #11745276, … |
| maximal normal subgroup of | D8×D29, #11745273, #11745276, … |
| maximal quotient of | #11745155, #11745157, #11745174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(464, 15);