Finite Group DatabasebetaFinite Group Databasebeta| order | 292 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C73 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73 | C4 |
| prime radical, cosocle | D73 | C2 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 73 |
A minimal faithful permutation representation — 2 generators on 73 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)(32,47,48,60)(36,51,52,61)(40,49,55,57)(44,58,59,54)(46,62,63,50)(53,64,65,69)(56,66,67,70)(68,71,72,73);(1,2,5,10,19,32,49,34,17,29,44,60,69,73,72,67,55,39,26,15,24,37,54,62,42,25,12,3,7,14,23,36,53,66,51,30,46,63,45,61,70,65,52,35,22,13,6,11,20,33,50,58,38,21,8,16,27,40,56,68,71,64,47,59,43,28,41,57,48,31,18,9,4)Polycyclic presentation:
2^2,73|a^2=b,c^a=c^27,c^b=c^7222 conjugacy classes — view the full character table.
| maximal subgroup of | #10596842, C2×#64408, #64408⋊C3, … |
| maximal normal subgroup of | #10596842, C2×#64408, #64408⋊C3, … |
| maximal quotient of | #10596833, C2×#64408, C3×#64408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(292, 3);