Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#16864520 |
| derived, Sylow | C541 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14524194 |
| commutator, hypocenter | C541 | C4×C8 |
| Frattini | C22 | C2×#14524194 |
| Fitting | C2×C4×C541 | C4 |
| socle, prime radical | C22×C541 | C2×C4 |
| cosocle | C2×Dic541 | C22 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2×C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
1112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16864520, #46831016, #16864520⋊C8, … |
| maximal normal subgroup of | C8×#16864520, #46831016, #16864520⋊C8, … |
| maximal quotient of | C8×#16864520, #46831016, #46831041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 199);