Finite Group DatabasebetaFinite Group Databasebeta| order | 952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C7×C17 ⋊ D4 |
| Sylow | C17 ⋊ D28 |
| Sylow | C7 ⋊ C22⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D17 |
| commutator, Fitting, socle, cosocle | C2×C7×C17 | C22 |
| hypocenter | C7×C17 | D4 |
| LCS | G ▷ C2×C7×C17 ▷ C7×C17 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 476 |
Polycyclic presentation:
2^3,7,17|a^2=c,b^a=bc,e^a=e^16,d^b=d^697 conjugacy classes — view the full character table.
| maximal subgroup of | #14274132, #14274133, #14274135, … |
| maximal normal subgroup of | #14274132, #14274133, #14274135, … |
| maximal quotient of | #14274032, #14274037, #14274038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(952, 12);