Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C7×#41 ⋊ C2 |
| Hall | C3×C7 ⋊ 2−1+4 |
| Sylow | C7 ⋊ #1010 |
| Sylow | C3 ⋊ #6554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D21 |
| commutator, socle, cosocle | C2×C3×C7 | C24 |
| Fitting | C3×C7×#41 | C2 |
| hypercenter | #41 | D21 |
| hypocenter | C3×C7 | 2−1+4 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C2 ◁ #41 | |
292 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^5,3,7|b^2=e,c^2=e,d^2=e,d^a=de,f^a=f^2,g^a=g^6,c^b=ce117 conjugacy classes — view the full character table.
| maximal subgroup of | #13054802, #13054803, #13054837, … |
| maximal normal subgroup of | #13054802, #13054803, #13054837, … |
| maximal quotient of | #13061606, #13061608, #13061610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1245);