Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | M16×C109 ⋊ C4 |
| Sylow | C109 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#89137 |
| commutator, socle | C2×C109 | C2×C42 |
| Fitting | M16×C109 | C4 |
| hypercenter | M16 | #89137 |
| hypocenter | C109 | #405 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C4 ◁ M16 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,d^2=f,g^a=g^76,c^b=cf,g^b=g^33,g^d=g^108,g^e=g^108310 conjugacy classes — view the full character table.
| maximal subgroup of | #28378789, #28378791, #28378808, … |
| maximal normal subgroup of | #28378789, #28378791, #28378808, … |
| maximal quotient of | M16×#11724786, #28378230, #28378237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1515);