Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C17 ⋊ C2 |
| Sylow | C17 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D17 |
| commutator, socle, cosocle | C2×C17 | C24 |
| Fitting | #41×C17 | C2 |
| hypercenter | #41 | D17 |
| hypocenter | C17 | H(5,𝔽2) |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
Polycyclic presentation:
2^5,17|d^2=e,d^a=de,f^a=f^16,c^b=ce97 conjugacy classes — view the full character table.
| maximal subgroup of | #11762975, #11762978, #11762985, … |
| maximal normal subgroup of | #11762975, #11762978, #11762985, … |
| maximal quotient of | #11763281, #11763283, #11763289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 232);