Finite Group DatabasebetaFinite Group Databasebeta| order | 404 |
| isoclinism | isoclinic class of #87938 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C101 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C101 | C4 |
| prime radical, cosocle | D101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 101 |
A minimal faithful permutation representation — 2 generators on 101 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,65)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,49,63,50)(53,66,67,80)(57,70,71,77)(61,74,75,73)(64,68,78,69)(72,81,82,91)(76,85,86,88)(79,83,89,84)(87,92,93,98)(90,94,96,95)(97,99,100,101);(1,2,5,10,19,32,49,42,25,12,3,7,14,23,36,53,68,59,38,21,8,16,27,40,57,72,83,74,55,34,17,29,44,61,76,87,94,85,70,51,30,46,64,79,90,97,99,92,81,66,47,65,80,91,98,101,100,96,89,78,63,45,62,77,88,95,93,86,75,60,43,28,41,58,73,84,82,71,56,39,26,15,24,37,54,69,67,52,35,22,13,6,11,20,33,50,48,31,18,9,4)Polycyclic presentation:
2^2,101|a^2=b,c^a=c^10,c^b=c^10029 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#87938, C3×#87938, C3⋊#87938, … |
| maximal normal subgroup of | C2×#87938, C3×#87938, #87938⋊C5, … |
| maximal quotient of | #11717581, C2×#87938, C3×#87938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(404, 3);