Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#2209 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C37 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C37 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C42×C37 ◁ C4×C8×C37 ◁ G | |
154 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 4736 |
A minimal faithful permutation representation — 3 generators on 73 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)(39,41)(42,43,47,51)(44,52,55,71)(45,56,60,70)(46,61,58,50)(48,63,65,53)(49,66,68,59)(54,72,62,67)(57,69,73,64);(38,39,40,41);(42,44,47,55)(43,48,51,65)(45,57,60,73)(46,62,58,54)(49,67,68,72)(50,69,61,64)(52,70,71,56)(53,66,63,59)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#12321, C37×#12322, C37×#12327, … |
| maximal normal subgroup of | C37×#12321, C37×#12322, C37×#12327, … |
| maximal quotient of | C37×#12421, C37×#12427, C37×#12448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 941);