Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#2860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C22×D4×C37 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
516 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 216 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)(43,44)(47,48)(52,55)(53,57);(42,43,46,44)(45,47,49,48)(50,51,54,56)(52,53,55,57);(38,39,40,41)(42,44,46,43)(45,48,49,47)(50,52,54,55)(51,53,56,57);(42,45,46,49)(43,47,44,48)(50,53)(51,55)(52,56)(54,57)1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#7666, C37×#7672, C37×#7686, … |
| maximal normal subgroup of | C37×#7666, C37×#7672, C37×#7686, … |
| maximal quotient of | C37×#14688, C37×#14699, C37×#14700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1592);