Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C26 |
| direct product | C23×#2366 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C24 |
| commutator | C22 | C23×C4×C23 |
| Frattini, cosocle | C23 | C24×C23 |
| prime radical | C2×C23×#127 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ G | |
832 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 328 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,26)(29,31)(32,33,35,34);(25,26)(32,34,35,33);(28,29,30,31);(24,26,27,25)1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#8920, C23×#8921, C23×#8924, … |
| maximal normal subgroup of | C23×#8920, C23×#8921, C23×#8924, … |
| maximal quotient of | C4⋊C42×C23, C23×#13820, C23×#13824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1098);