Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2190 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#2191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C17×#575 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×M16×C17 ◁ G | |
216 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,27)(20,28,30,46)(21,32,34,48)(22,37,35,26)(24,39,40,29)(25,42,44,36)(31,47,38,43)(33,45,49,41);(18,20)(19,24)(21,33)(22,38)(23,30)(25,43)(26,45)(27,40)(28,32)(29,36)(31,35)(34,49)(37,41)(39,42)(44,47)(46,48);(21,34)(25,44)(28,46)(29,39)(32,48)(33,49)(36,42)(43,47)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 923);