Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C26 |
| direct product | C37×#3004 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| prime radical | C37×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G | |
738 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 738 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) = 1184 |
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)(38,39)(40,41)(42,43)(44,50)(45,53)(46,48)(47,51)(49,55)(52,57)(54,56);(42,44,46,52)(43,47,48,56)(45,54,55,51)(49,57,53,50);(39,41);(43,48)(47,56)(49,53)(50,57)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9519, C37×#18136, C37×#18146, … |
| maximal normal subgroup of | C37×#9519, C37×#18136, C37×#18146, … |
| maximal quotient of | C37×#18133, C37×#18138, C37×#18143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1736);