Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C179 ⋊ #395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D179 |
| commutator, socle, prime radical, cosocle | C23×C179 | C23 |
| Fitting | C22×Q8×C179 | C2 |
| hypercenter | C22×Q8 | D179 |
| hypocenter | C179 | #395 |
| LCS | G ▷ C23×C179 ▷ C179 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
182 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^1781802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507960, #37507962, #37507967, … |
| maximal normal subgroup of | #37507960, #37507962, #37507967, … |
| maximal quotient of | #37507250, #37507263, #37507271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 468);