Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D541⋊C8 |
| unambiguous semidirect product | D541⋊(C2×C8) |
| derived, Sylow | C541 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14524194 |
| commutator, hypocenter | C541 | C22×C8 |
| Frattini | C2 | C22×#14524194 |
| Fitting | C2×C4×C541 | C4 |
| socle | C22×C541 | C2×C4 |
| prime radical | C22×D541 | C4 |
| cosocle | Dic541 | C23 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
1112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×#14524194)⋊C8, #46831048, #46831050, … |
| maximal normal subgroup of | (C2×#14524194)⋊C8, #46831048, #46831050, … |
| maximal quotient of | C2×C4×#16864520, C4×D541⋊C8, D541⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 229);