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D9×C53⋊C13 #27137149

order12402
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productD9×C53⋊C13
unambiguous semidirect productC9⋊(C2×C53⋊C13)
unambiguous semidirect product(D9×C53)⋊C13

Splittings

Fitting, derived, HallC9×C53 ⋊ C2×C13
HallC9×C53⋊C13 ⋊ C2
HallD9×C53 ⋊ C13
SylowC53 ⋊ C13×D9
SylowC9 ⋊ C2×C53⋊C13

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C53C2×C13
FrattiniC3D3×C53⋊C13
socleC3×C53D3×C13
LCSG ▷ C9×C53
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 477

A minimal faithful permutation representation — 2 generators on 62 points:

(2,3,5,9,17,32,48,29,46,25,19,34,51)(4,7,13,24,8,15,28,10,18,23,39,53,40)(6,11,20,35,43,41,37,52,49,33,50,16,30)(12,22,38,31,45,21,36,27,44,47,14,26,42)(55,57)(56,60)(58,61)(59,62);(1,2,4,8,16,31,20,11,21,37,51,30,47,48,44,9,3,6,12,23,40,42,36,22,32,49,28,45,17,33,24,18,7,14,27,13,25,41,52,39,50,53,46,35,5,10,19,34,15,29,38,26,43)(54,59,57,56,61,58,60,55,62)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×D53⋊C13, C2×D9×C53⋊C13
maximal normal subgroup ofD9×D53⋊C13, C2×D9×C53⋊C13
maximal quotient ofDic9×C53⋊C13, C2×D9×C53⋊C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12402, 12);