Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C22×C42 |
| direct product | C37×#2818 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
630 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 630 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) = 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)(42,43)(44,47)(45,46)(48,49)(50,51,53,54)(52,55,57,56);(39,41)(43,46)(44,48)(51,54)(55,56);(38,39)(40,41)(42,43)(44,49)(45,46)(47,48)(50,51)(52,56)(53,54)(55,57);(42,44,45,48)(43,47,46,49)(50,52,53,57)(51,55,54,56)962 conjugacy classes — view the full character table.
| maximal subgroup of | C37×#18462, C37×#18464, C2×C37×#2818, … |
| maximal normal subgroup of | C37×#18462, C37×#18464, C2×C37×#2818, … |
| maximal quotient of | C37×#14623, C37×#14624, C37×#14661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1550);