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C5×C23⋊(D19⋊C3) #27189983

order13110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23⋊(D19⋊C3)
unambiguous semidirect productC23⋊(C5×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C5×D23)
unambiguous semidirect productD437⋊(C3×C5)
unambiguous semidirect product(C5×D437)⋊C3

Splittings

Fitting, socle, HallC5×C19×C23 ⋊ C2×C3
derived, HallC19×C23 ⋊ C2×C3×C5
HallC5×C23×C19⋊C3 ⋊ C2
HallC5×D437 ⋊ C3
HallC23×C19⋊C3 ⋊ C2×C5
HallD437 ⋊ C3×C5
HallC5×C19⋊C3 ⋊ D23
HallC5×C23 ⋊ D19⋊C3
HallC5×C19 ⋊ C3×D23
HallC19⋊C3 ⋊ C5×D23
SylowC23 ⋊ C5×D19⋊C3
SylowC19 ⋊ C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC5C23⋊(D19⋊C3)
commutator, cosocle, hypocenterC19×C23C2×C3×C5
FrattiniC1G
Fitting, socleC5×C19×C23C2×C3
LCSG ▷ C19×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 2185

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D23×D19⋊C3, D5×C23⋊(D19⋊C3), D115⋊(D19⋊C3), …
maximal normal subgroup ofC5×D23×D19⋊C3, D5×C23⋊(D19⋊C3), D115⋊(D19⋊C3), …
maximal quotient ofC5×C23⋊((C19⋊C3)⋊C4), C2×C5×C23⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13110, 20);