Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #11924339 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C7 |
No aliases for this group.
| Fitting, socle, derived | C22×C72 ⋊ C2×C3 |
| Hall | C22×C7⋊D7 ⋊ C3 |
| Sylow | C72 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C72 | C2×C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 42 |
Polycyclic presentation:
2,3,2^2,7^2|e^a=e^6,f^a=f^6,c^b=cd,d^b=c,e^b=e^2,f^b=f^440 conjugacy classes — view the full character table.
| maximal subgroup of | #72222158, #72222160, A4×#64425, … |
| maximal normal subgroup of | #72222158, #72222160, A4×#64425, … |
| maximal quotient of | C2×#11924339, #72222274 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 254);