Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting, socle, Sylow | C292 ⋊ Dic3 |
| derived, Hall | C292⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C292⋊C3 | C4 |
| Fitting, socle | C292 | Dic3 |
| prime radical, cosocle | (C29⋊D29)⋊C3 | C2 |
| LCS | G ▷ C292⋊C3 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,29^2|a^2=b,c^a=c^2,d^a=d^19e^22,e^a=d^2e^10,d^b=d^28,e^b=e^28,d^c=d^4e^26,e^c=d^7e^2476 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#23758666, C3⋊#23758666 |
| maximal normal subgroup of | C3×#23758666 |
| maximal quotient of | #44475585, C3×#23758666, C3⋊#23758666 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 24);