Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C277 ⋊ C2 |
| Sylow | C277 ⋊ #555 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | C4⋊Q8×C277 | C2 |
| hypercenter | C4⋊Q8 | D277 |
| hypocenter | C277 | #555 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|b^2=f,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^276,d^b=de,g^b=g^276,g^c=g^2761957 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47982248, #47982251, #47982310, … |
| maximal normal subgroup of | #47982248, #47982251, #47982310, … |
| maximal quotient of | #47986051, #47986118, #47986204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1265);