Finite Group DatabasebetaFinite Group Databasebeta| order | 18608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C1163 ⋊ C2 |
| Sylow | C1163 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1163 |
| commutator, socle, cosocle | C2×C1163 | C23 |
| Fitting | D4×C1163 | C2 |
| hypercenter | D4 | D1163 |
| hypocenter | C1163 | #41 |
| LCS | G ▷ C2×C1163 ▷ C1163 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9304 |
Polycyclic presentation:
2^4,1163|c^2=d,b^a=bd,e^c=e^11622915 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49151818, #49151820, #49151823, … |
| maximal normal subgroup of | #49151818, #49151820, #49151823, … |
| maximal quotient of | #49151755, #49151757, (C22⋊D1163)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18608, 39);