Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×#6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C34 |
| direct product | D4×#6911 |
| unambiguous semidirect product | C4⋊(C2×#6911) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C22×C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C2×C32 | C22×C33 |
| LCS | G ▷ C2×C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C33×D4 ◁ G | |
640 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4)(5,6,9)(7,13,18)(8,12,19)(10,20,16)(11,23,17)(14,25,28)(15,22,29)(21,31,27)(24,30,26);(2,4)(5,7,14,17,15,27,8,16,26)(6,10,21,11,13,24,12,22,25)(9,18,28,23,29,31,19,20,30);(7,15,16)(10,13,22)(14,26,27)(18,29,20)(21,25,24)(28,30,31)175 conjugacy classes — view the full character table.
| Fitting subgroup of | D4×#92333, D4×#92285, D4×#4179⋊C3, … |
| maximal subgroup of | D4×#10624749, D4×#92333, D4×#92285, … |
| maximal normal subgroup of | D4×#10624749, D4×#92333, D4×#92285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2220);