Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#14524194 |
| Fitting | Q8×C541 ⋊ C4 |
| Sylow | C541 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#14524194 |
| commutator, socle | C2×C541 | C22×C4 |
| Fitting | Q8×C541 | C4 |
| prime radical, cosocle | C2×D541 | C23 |
| hypercenter | Q8 | #14524194 |
| hypocenter | C541 | C4×Q8 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×#14524194, Q16×#14524194, #46831214, … |
| maximal normal subgroup of | SD16×#14524194, Q16×#14524194, #46831214, … |
| maximal quotient of | C4⋊C4×#14524194, #46831124, #46831126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 227);