Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#11763471 |
| Fitting | C2×C4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×#548 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D17 |
| commutator, cosocle | C22×C17 | C25 |
| Frattini | C22 | C24×D17 |
| Fitting | C2×C4×Q8×C17 | C2 |
| socle | C23×C17 | C24 |
| hypercenter | C2×C4×Q8 | D17 |
| hypocenter | C17 | C2×#548 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16925956, #17000620, #17049700, … |
| maximal normal subgroup of | #16925956, #17000620, #17049700, … |
| maximal quotient of | C2×Q8×#63227, C2×#14531622, C2×#14531705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17979);