Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3055 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24×C4 |
| direct product | C37×#3152 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C37×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G | |
552 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 4 generators on 57 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)(42,43,46,49)(44,50,51,57)(45,53,54,48)(47,55,56,52);(42,44,45,52,46,51,54,55)(43,47,48,50,49,56,53,57);(38,39,40,41);(44,51)(47,56)(50,57)(52,55)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9421, C37×#9429, C37×#9435, … |
| maximal normal subgroup of | C37×#9421, C37×#9429, C37×#9435, … |
| maximal quotient of | C37×#19622, C37×#19626, C37×#19630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1884);