Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#2199 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C17 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×D4×C17 ◁ G | |
270 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33);(18,20)(19,23)(21,28)(22,27)(24,26)(25,30)(29,33)(31,32);(20,27)(21,29)(23,30)(26,32)289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 931);