Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24×C4 |
| direct product | C37×#3147 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| socle | C22×C37 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G | |
572 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 572 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)(44,51)(45,49)(46,55)(47,50)(48,53)(52,56)(54,57);(42,44,46,53,47,54,45,52)(43,48,49,51,50,56,55,57);(38,39,40,41);(42,45,47,46)(43,49,50,55)(44,52,54,53)(48,51,56,57)1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9069, C37×#9750, C37×#9753, … |
| maximal normal subgroup of | C37×#9069, C37×#9750, C37×#9753, … |
| maximal quotient of | C37×#19596, C37×#19600, C37×#19603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1879);