Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2169 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#3633 |
| commutator, socle | C22×C17 | C22×C8 |
| Fitting, prime radical | C2×D4×C17 | C8 |
| cosocle | C2×#3624 | C23 |
| hypercenter | C2×D4 | #3633 |
| hypocenter | C17 | #2169 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^8,c^b=cg,h^c=h^9,h^e=h^13,h^f=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | #17982279, #17982280, #17982281, … |
| maximal normal subgroup of | #17982279, #17982280, #17982281, … |
| maximal quotient of | #17982283, #17982310, #17982321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21726);