Finite Group DatabasebetaFinite Group Databasebeta| order | 4736 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C37 · Schur multiplier (H2) = C25 |
| direct product | C37×#2621 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C37 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C37 |
| prime radical | C24×C37 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C37 ◁ G | |
528 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 528 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) = 61 |
| transitive degree | μt(G) = 2368 |
A minimal faithful permutation representation — 4 generators on 61 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)(42,43,44,45)(47,51)(52,54)(53,59)(60,61);(39,41)(46,47)(48,54)(49,53)(50,51)(52,56)(55,61)(57,60)(58,59);(38,39)(40,41)(42,43)(44,45)(46,48,50,56)(47,52,51,54)(49,57,58,55)(53,61,59,60);(46,49,50,58)(47,53,51,59)(48,55,56,57)(52,60,54,61)1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#9195, C37×#9196, C37×#11694, … |
| maximal normal subgroup of | C37×#9195, C37×#9196, C37×#11694, … |
| maximal quotient of | C37×#14258, C37×#14261, C37×#14274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 1353);