Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#2239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| prime radical | C23×C37 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×M16×C37 ◁ G | |
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 69 |
| transitive degree | μt(G) = 1184 |
A minimal faithful permutation representation — 3 generators on 69 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,43,47)(40,48,49,66)(41,52,53,69)(42,57,55,46)(44,59,60,50)(45,62,63,56)(51,64,58,67)(54,61,68,65);(41,53)(45,63)(48,66)(50,59)(52,69)(54,68)(56,62)(64,67);(38,40,42,58,43,49,55,51)(39,44,46,65,47,60,57,61)(41,54,56,59,53,68,62,50)(45,64,52,66,63,67,69,48)740 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#12299, C37×#12300, C37×#12302, … |
| maximal normal subgroup of | C37×#12299, C37×#12300, C37×#12302, … |
| maximal quotient of | C37×#12875, C37×#12931, C37×#13009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 971);