Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#2205 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C17 |
| prime radical | C17×2−1+4 | C22 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×Q8×C17 ◁ G | |
224 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,31)(22,26)(23,33)(24,29)(25,30)(27,32);(18,20,24,23)(19,25,29,31)(21,32,30,22)(26,28,27,33);(18,21,24,30)(19,26,29,27)(20,22,23,32)(25,33,31,28)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 937);