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D465 #11745394

order930
isoclinismisoclinic class of D465
automorphismAut(G) order 111600
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD465
unambiguous semidirect productC3⋊D155
unambiguous semidirect productC5⋊D93
unambiguous semidirect productC31⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C31 ⋊ C2
HallC5×C31 ⋊ D3
HallC3×C31 ⋊ D5
SylowC31 ⋊ D15
HallC3×C5 ⋊ D31
SylowC5 ⋊ D93
SylowC3 ⋊ D155

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C31C2
LCSG ▷ C3×C5×C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 465

A minimal faithful permutation representation — 2 generators on 39 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);(2,3)(5,8)(6,7)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Polycyclic presentation:

2,3,5,31|b^a=b^2,c^a=c^4,d^a=d^30

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD15×D31, D5×D93, D3×D155, …
maximal normal subgroup ofD15×D31, D5×D93, D3×D155, …
maximal quotient ofDic465, C2×D465, D1395, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(930, 17);