Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #2108 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#3633 |
| commutator, socle | C2×C17 | C2×C4×C8 |
| Fitting | M16×C17 | C8 |
| prime radical | C22×D17 | C2×C8 |
| cosocle | #63242 | C23 |
| hypercenter | M16 | #3633 |
| hypocenter | C17 | #2108 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ M16 | |
184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,f^2=g,h^a=h^9,c^b=cg,h^b=h^4,h^d=h^13,h^e=h^16,h^f=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17982450, #17982452, #17982454, … |
| maximal normal subgroup of | #17982450, #17982452, #17982454, … |
| maximal quotient of | #17981822, #17981823, #17981829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21673);