Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | Q8×#3861 |
| Fitting, Hall | C72×Q8 ⋊ C3 |
| Sylow | C72 ⋊ C3×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#3861 |
| commutator, socle, cosocle | C2×C72 | C22×C3 |
| Fitting | C72×Q8 | C3 |
| prime radical | C2×#3861 | C22 |
| hypercenter | Q8 | #3861 |
| hypocenter | C72 | C3×Q8 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#3861, #72228711, Q8×#64424, … |
| maximal normal subgroup of | SD16×#3861, #72228711, Q8×#64424, … |
| maximal quotient of | C4⋊C4×#3861, C2×Q8×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 176);