Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C32×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ #624 |
| Sylow | C32 ⋊ C2×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C3⋊D3)⋊D13 |
| commutator, hypocenter | C32×C13 | C2×C4 |
| Fitting, socle, cosocle | C2×C32×C13 | C22 |
| prime radical | C2×C13×C3⋊D3 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C2 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2^3,3^2,13|a^2=c,d^a=d^2,f^a=f^12,d^b=d^2,e^b=e^290 conjugacy classes — view the full character table.
| maximal subgroup of | D32⋊Dic13, #14273042, #14273047, … |
| maximal normal subgroup of | D32⋊Dic13, #14273042, #14273047, … |
| maximal quotient of | #14272794, #14272796, #14272804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 130);