Finite Group DatabasebetaFinite Group Databasebeta| order | 464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C29 ⋊ C2 |
| Sylow | C29 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D29 |
| commutator, socle, cosocle | C2×C29 | C23 |
| Fitting | D4×C29 | C2 |
| hypercenter | D4 | D29 |
| hypocenter | C29 | #41 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 232 |
A minimal faithful permutation representation — 3 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)(31,35)(32,36);(30,32,33,36)(31,34,35,37);(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)(33,35)(36,37)Polycyclic presentation:
2^4,29|b^2=d,c^a=cd,e^a=e^28,c^b=cd80 conjugacy classes — view the full character table.
| maximal subgroup of | #11745224, #11745273, #11745274, … |
| maximal normal subgroup of | #11745224, #11745273, #11745274, … |
| maximal quotient of | #11745239, #11745240, #11745241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(464, 40);