Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#3633 |
| Fitting, socle | C22×C17 ⋊ C8 |
| derived, Sylow | C17 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #3633 |
| commutator, hypocenter | C17 | C22×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C17 | C8 |
| prime radical | C22×D17 | C4 |
| cosocle | #595 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 68 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#3633)⋊C4, C2×C4×#3633, C2×C22⋊#3633, … |
| maximal normal subgroup of | (C2×#3633)⋊C4, C2×C4×#3633, C2×C22⋊#3633, … |
| maximal quotient of | C2×C4×#3633, C2×C22⋊#3633, C2×C4⋊#3633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 243);