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D595 #11924737

order1190
isoclinismisoclinic class of D595
automorphismAut(G) order 228480
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD595
unambiguous semidirect productC5⋊D119
unambiguous semidirect productC7⋊D85
unambiguous semidirect productC17⋊D35

Splittings

Fitting, socle, derived, HallC5×C7×C17 ⋊ C2
HallC7×C17 ⋊ D5
HallC5×C17 ⋊ D7
HallC5×C7 ⋊ D17
SylowC17 ⋊ D35
SylowC7 ⋊ D85
SylowC5 ⋊ D119

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C17C2
LCSG ▷ C5×C7×C17
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 595

A minimal faithful permutation representation — 2 generators on 29 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);(2,5)(3,4)(7,12)(8,11)(9,10)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

Polycyclic presentation:

2,5,7,17|b^a=b^4,c^a=c^6,d^a=d^16

Conjugacy classes & character table

299 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×D35, D7×D85, D5×D119, …
maximal normal subgroup ofD17×D35, D7×D85, D5×D119, …
maximal quotient ofDic595, C2×D595, C3×D595, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1190, 7);