Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2404 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C22×C22⋊C4×C17 | C2 |
| hypercenter | C22×C22⋊C4 | D17 |
| hypocenter | C17 | #2404 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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|b^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^16,c^b=cg358 conjugacy classes — view the full character table.
| maximal subgroup of | #16932121, #16932123, #16932141, … |
| maximal normal subgroup of | #16932121, #16932123, #16932141, … |
| maximal quotient of | #16956201, #16957009, #16957094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7829);