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C2×D8151 #45656838

order32604
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16302
direct productC2×D8151
unambiguous semidirect product(C2×C3)⋊D2717
unambiguous semidirect product(C2×C11)⋊D741
unambiguous semidirect product(C2×C13)⋊D627
unambiguous semidirect product(C2×C19)⋊D429

Splittings

Fitting, socleC2×C3×C11×C13×C19 ⋊ C2
derived, HallC3×C11×C13×C19 ⋊ C22
HallC11×C13×C19 ⋊ C2×D3
HallC3×C13×C19 ⋊ C2×D11
HallC3×C11×C19 ⋊ C2×D13
HallC3×C11×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×D33
HallC11×C19 ⋊ C2×D39
HallC11×C13 ⋊ C2×D57
HallC3×C19 ⋊ C2×D143
HallC3×C13 ⋊ C2×D209
HallC3×C11 ⋊ C2×D247
SylowC19 ⋊ C2×D429
SylowC13 ⋊ C2×D627
SylowC11 ⋊ C2×D741
SylowC3 ⋊ C2×D2717

Subgroups

subgroupG/H
center, hypercenterC2D8151
commutator, cosocle, hypocenterC3×C11×C13×C19C22
FrattiniC1G
Fitting, socleC2×C3×C11×C13×C19C2
LCSG ▷ C3×C11×C13×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 16302

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(4,5)(7,16)(8,15)(9,14)(10,13)(11,12)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)

Conjugacy classes & character table

8154 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32604
maximal normal subgroup ofD32604
maximal quotient ofDic16302, D32604

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 188);