Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C292⋊C3 ⋊ C4 |
| Sylow | C292 ⋊ Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19097943 |
| commutator, hypocenter | C292⋊C3 | C4 |
| Fitting, socle | C2×C292 | D3 |
| prime radical, cosocle | C2×C292⋊C3 | C2 |
| LCS | G ▷ C292⋊C3 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29^2,2|a^2=e,b^a=b^2,d^a=c^5d^28,c^b=c^8d^14,d^b=cd^20370 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#23758656, C3⋊#23758656 |
| maximal normal subgroup of | C3×#23758656 |
| maximal quotient of | #44475575, C3×#23758656, C3⋊#23758656 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 14);