Finite Group DatabasebetaFinite Group Databasebeta| order | 3776 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#452 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C59 |
| prime radical | C2×#41×C59 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 3 generators on 79 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)(64,65,69,72)(66,73,75,78)(67,71,68,76)(70,77,79,74);(64,66)(65,70)(67,74)(68,77)(69,75)(71,78)(72,79)(73,76);(61,63)(64,67,69,68)(65,71,72,76)(66,74,75,77)(70,78,79,73)1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C59×#452, C59×#3002, C59×#3005, … |
| maximal normal subgroup of | C2×C59×#452, C59×#3002, C59×#3005, … |
| maximal quotient of | C59×#1603, C59×#1606, C59×#1615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3776, 133);