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C23×C5⋊(D19⋊C3) #27189986

order13110
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C5⋊(D19⋊C3)
unambiguous semidirect productC5⋊(C23×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D5×C23)
unambiguous semidirect productD95⋊(C3×C23)
unambiguous semidirect product(C23×D95)⋊C3

Splittings

Fitting, socle, HallC5×C19×C23 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C3×C23
HallC5×C23×C19⋊C3 ⋊ C2
HallC23×D95 ⋊ C3
HallC23×C19⋊C3 ⋊ D5
HallC19×C23 ⋊ C3×D5
HallC5×C19⋊C3 ⋊ C2×C23
HallD95 ⋊ C3×C23
HallC5×C23 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D5×C23
SylowC19 ⋊ C3×D5×C23
SylowC5 ⋊ C23×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC23C5⋊(D19⋊C3)
commutator, cosocle, hypocenterC5×C19C2×C3×C23
FrattiniC1G
Fitting, socleC5×C19×C23C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C23

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:

(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(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);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(20,21,23,24,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD23×C5⋊(D19⋊C3), D5×C23×D19⋊C3, D115⋊(D19⋊C3), …
maximal normal subgroup ofD23×C5⋊(D19⋊C3), D5×C23×D19⋊C3, D115⋊(D19⋊C3), …
maximal quotient ofC23×(C19⋊C3)⋊Dic5, C2×C23×C5⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13110, 23);