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C2×D7905 #44539411

order31620
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15810
direct productC2×D7905
unambiguous semidirect product(C2×C3)⋊D2635
unambiguous semidirect product(C2×C5)⋊D1581
unambiguous semidirect product(C2×C17)⋊D465
unambiguous semidirect product(C2×C31)⋊D255

Splittings

Fitting, socleC2×C3×C5×C17×C31 ⋊ C2
derived, HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C2×D3
HallC3×C17×C31 ⋊ C2×D5
HallC17×C31 ⋊ C2×D15
HallC3×C5×C31 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D31
HallC5×C31 ⋊ C2×D51
HallC3×C31 ⋊ C2×D85
HallC5×C17 ⋊ C2×D93
HallC3×C17 ⋊ C2×D155
SylowC31 ⋊ C2×D255
SylowC17 ⋊ C2×D465
HallC3×C5 ⋊ C2×D527
SylowC5 ⋊ C2×D1581
SylowC3 ⋊ C2×D2635

Subgroups

subgroupG/H
center, hypercenterC2D7905
commutator, cosocle, hypocenterC3×C5×C17×C31C22
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C3×C5×C17×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 15810

A minimal faithful permutation representation — 2 generators on 58 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)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(4,5)(7,10)(8,9)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(29,58)(30,57)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

7908 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31620
maximal normal subgroup ofD31620
maximal quotient ofDic15810, D31620

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 168);