Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1374 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C23 | C22 |
| commutator | C2 | C4×C16×C23 |
| Frattini, cosocle | C22×C8 | C22×C23 |
| socle, prime radical | C23×C23 | C2×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C23 ◁ G | |
160 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 2 generators on 47 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)(32,33,34,37,35,38,40,43,36,39,41,44,42,45,46,47);(25,27)(28,29,30,31)1840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#7102, C23×#7112, C23×#7113, … |
| maximal normal subgroup of | C23×#7102, C23×#7112, C23×#7113, … |
| maximal quotient of | C23×#7136, C23×#7142, C23×#7145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 106);