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C5×C3⋊(C7⋊D91) #34062191

order19110
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×C3⋊(C7⋊D91)
unambiguous semidirect productC3⋊(C5×C7⋊D91)
unambiguous semidirect productC7⋊(C5×D273)
unambiguous semidirect productC13⋊(C5×C3⋊(C7⋊D7))

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C2
derived, HallC3×C72×C13 ⋊ C2×C5
HallC5×C72×C13 ⋊ D3
HallC3×C5×C72 ⋊ D13
HallC72×C13 ⋊ C5×D3
HallC5×C72 ⋊ D39
HallC3×C5×C13 ⋊ C7⋊D7
HallC3×C72 ⋊ C5×D13
HallC5×C13 ⋊ C3⋊(C7⋊D7)
SylowC72 ⋊ C5×D39
HallC3×C13 ⋊ C5×C7⋊D7
HallC3×C5 ⋊ C7⋊D91
SylowC13 ⋊ C5×C3⋊(C7⋊D7)
SylowC3 ⋊ C5×C7⋊D91

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C7⋊D91)
commutator, cosocle, hypocenterC3×C72×C13C2×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C2
LCSG ▷ C3×C72×C13
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 9555

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(20,21)(23,24)(25,26)(27,28)(30,31)(32,33)(34,35);(6,7,9,11,13,15,17,18,16,14,12,10,8)(19,20,21)(29,30,32,34,35,33,31);(22,23,25,27,28,26,24)

Conjugacy classes & character table

4785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D7×D273, C5×D21×D91, C5×D13×C3⋊(C7⋊D7), …
maximal normal subgroup ofC5×D7×D273, C5×D21×D91, C5×D13×C3⋊(C7⋊D7), …
maximal quotient ofC5×C3⋊(C7⋊Dic91), C2×C5×C3⋊(C7⋊D91)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 184);