Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×Dic382 |
| Sylow | C191 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D191 |
| commutator, socle, prime radical, cosocle | C22×C191 | C24 |
| Fitting | C4×Q8×C191 | C2 |
| hypercenter | C4×Q8 | D191 |
| hypocenter | C191 | Q82 |
| LCS | G ▷ C22×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
212 conjugacy classes of subgroups.
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571597, #37571600, #37571659, … |
| maximal normal subgroup of | #37571597, #37571600, #37571659, … |
| maximal quotient of | Q8×Dic191⋊C4, C4⋊C4×Dic382, Q8×C4⋊Dic191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1280);