Finite Group DatabasebetaFinite Group Databasebeta| order | 15138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C292⋊C9 ⋊ C2 |
| Sylow | C292 ⋊ D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C292⋊C9 | C2 |
| Frattini | C3 | #19097943 |
| Fitting, socle | C3×C292 | D3 |
| LCS | G ▷ C292⋊C9 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 261 |
Polycyclic presentation:
2,3,29^2,3|b^3=e^2,b^a=b^2e,d^a=c^5d^28,e^a=e^2,c^b=c^8d^14,d^b=cd^20468 conjugacy classes — view the full character table.
| maximal subgroup of | #29502829⋊C2, C2×#29502829 |
| maximal normal subgroup of | #29502829⋊C2, C2×#29502829 |
| maximal quotient of | #44475575, C2×#29502829 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15138, 12);