Finite Group DatabasebetaFinite Group Databasebeta| order | 3776 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C59 |
| socle | C22×C59 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ G | |
310 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 170 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 — 4 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)(61,63)(64,65)(66,69)(67,68)(70,71);(65,68)(69,71);(60,61,62,63);(64,66,67,70)(65,69,68,71)1652 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C59×#1480, C59×#1484, C59×#1492, … |
| maximal normal subgroup of | C59×#1480, C59×#1484, C59×#1492, … |
| maximal quotient of | C59×#2285, C59×#2293, C59×#2297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3776, 213);