Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C25 |
| direct product | C37×#3293 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C37 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ G | |
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 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 — 4 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)(38,39,45,50)(40,51,54,56)(41,53,46,60)(42,47,59,65)(43,49,44,48)(52,67,69,63)(55,68,62,57)(58,66,61,64);(38,40,45,54)(39,46,50,41)(42,57,59,68)(43,60,44,53)(47,63,65,67)(48,56,49,51)(52,61,69,58)(55,64,62,66);(38,41,45,46)(39,40,50,54)(42,55,59,62)(43,56,44,51)(47,52,65,69)(48,53,49,60)(57,66,68,64)(58,67,61,63);(38,42)(39,47)(40,52)(41,55)(43,61)(44,58)(45,59)(46,62)(48,66)(49,64)(50,65)(51,67)(53,68)(54,69)(56,63)(57,60)1073 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#12311, C37×#12313, C37×#12367, … |
| maximal normal subgroup of | C37×#12311, C37×#12313, C37×#12367, … |
| maximal quotient of | C37×#19887, C37×#19894, C37×#19902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 2025);