Finite Group DatabasebetaFinite Group Databasebeta| order | 3776 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22 |
| direct product | C59×#435 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C23 |
| commutator | C22 | C22×C4×C59 |
| Frattini, cosocle | C2×C4 | C23×C59 |
| socle | C22×C59 | C22×C4 |
| prime radical | C2×D4×C59 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ G | |
124 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 71 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)(60,61)(62,63)(64,65,67,66,68,69,71,70);(61,63);(64,66,67,69,68,70,71,65)1652 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C59×#435, C59×#2929, C59×#2930, … |
| maximal normal subgroup of | C2×C59×#435, C59×#2929, C59×#2930, … |
| maximal quotient of | C59×#1581, C59×#1582, C59×#1583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3776, 116);