Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#22575839 |
| derived, Sylow | C541 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14524194 |
| commutator, hypocenter | C541 | C2×C16 |
| Frattini | C4 | C2×#14524194 |
| Fitting | C2×C4×C541 | C4 |
| socle, prime radical | C22×C541 | C8 |
| cosocle | #16864513 | C22 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
1112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22575839, #46831061, #46831063, … |
| maximal normal subgroup of | C4×#22575839, #46831061, #46831063, … |
| maximal quotient of | C4×#22575839, C22⋊#22575839, C4⋊#22575839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 218);