Finite Group DatabasebetaFinite Group Databasebeta| order | 2752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | #120×C43 ⋊ C2 |
| Sylow | C43 ⋊ H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Fitting | #120×C43 | C2 |
| hypercenter | #120 | D43 |
| hypocenter | C43 | H(3,𝔽4) |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #120 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 688 |
Polycyclic presentation:
2^6,43|a^2=e,b^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,g^b=g^42313 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2752, 1292);