Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | M16×C17 ⋊ C4 |
| Sylow | C17 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#595 |
| commutator, socle | C2×C17 | C2×C42 |
| Fitting | M16×C17 | C4 |
| prime radical | C22×D17 | C2×C4 |
| cosocle | C4×D17 | C23 |
| hypercenter | M16 | #595 |
| hypocenter | C17 | #405 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ M16 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^6,17|a^2=d,b^2=e,d^2=f,g^a=g^4,c^b=cf,g^b=g^13,g^d=g^16,g^e=g^1680 conjugacy classes — view the full character table.
| maximal subgroup of | #14544541, #14544543, #14544560, … |
| maximal normal subgroup of | #14544541, #14544543, #14544560, … |
| maximal quotient of | M16×#3624, #14543982, #14543989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1515);