Finite Group DatabasebetaFinite Group Databasebeta| order | 272 |
| isoclinism | isoclinic class of Dic34 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D17 |
| commutator, socle, cosocle | C2×C17 | C23 |
| Frattini | C2 | C22×D17 |
| Fitting | C2×C4×C17 | C2 |
| hypercenter | C2×C4 | D17 |
| hypocenter | C17 | #41 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 136 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(19,23)(22,25);(18,20,21,24)(19,22,23,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,22)(21,23)(24,25)Polycyclic presentation:
2^4,17|b^2=d,c^a=cd,e^a=e^1674 conjugacy classes — view the full character table.
| maximal subgroup of | #10587476, #10587496, #10587587, … |
| maximal normal subgroup of | #10587476, #10587496, #10587587, … |
| maximal quotient of | C4×Dic34, #10587556, #10587558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(272, 39);