Finite Group DatabasebetaFinite Group Databasebeta| order | 11296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19150738 |
| Fitting | C2×Q8×C353 ⋊ C2 |
| Sylow | C353 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D353 |
| commutator, cosocle | C2×C353 | C24 |
| Frattini | C2 | C23×D353 |
| Fitting | C2×Q8×C353 | C2 |
| socle | C22×C353 | C23 |
| hypercenter | C2×Q8 | D353 |
| hypocenter | C353 | C2×#41 |
| LCS | G ▷ C2×C353 ▷ C353 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
1780 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36377770, #36377782, #36377787, … |
| maximal normal subgroup of | #36377770, #36377782, #36377787, … |
| maximal quotient of | C2×#26014950, C2×#26014954, C2×Q8×Dic353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11296, 190);