Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #2792 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, prime radical, cosocle | C23×C17 | C24 |
| Fitting | C17×#384 | C2 |
| hypercenter | #384 | D17 |
| hypocenter | C17 | #2792 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #384 | |
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=efg,b^2=e,c^2=f,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #16946688, #16946692, #16947274, … |
| maximal normal subgroup of | #16946688, #16946692, #16947274, … |
| maximal quotient of | #16962307, #16962876, #16962932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12306);