Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | M16×C41 ⋊ C4 |
| Sylow | C41 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#4223 |
| commutator, socle | C2×C41 | C2×C42 |
| Fitting | M16×C41 | C4 |
| prime radical | C22×D41 | C2×C4 |
| cosocle | C4×D41 | C23 |
| hypercenter | M16 | #4223 |
| hypocenter | C41 | #405 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C4 ◁ M16 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^6,41|a^2=d,b^2=e,d^2=f,g^a=g^9,c^b=cf,g^b=g^32,g^d=g^40,g^e=g^40140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1515);