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C3×C5⋊(C7⋊D91) #34062197

order19110
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5⋊(C7⋊D91)
unambiguous semidirect productC5⋊(C3×C7⋊D91)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C2
derived, HallC5×C72×C13 ⋊ C2×C3
HallC3×C72×C13 ⋊ D5
HallC3×C5×C72 ⋊ D13
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ C3×D13
HallC3×C5×C13 ⋊ C7⋊D7
HallC3×C72 ⋊ D65
HallC5×C13 ⋊ C3×C7⋊D7
SylowC72 ⋊ C3×D65
HallC3×C13 ⋊ C5⋊(C7⋊D7)
HallC3×C5 ⋊ C7⋊D91
SylowC13 ⋊ C3×C5⋊(C7⋊D7)
SylowC5 ⋊ C3×C7⋊D91

Subgroups

subgroupG/H
center, hypercenterC3C5⋊(C7⋊D91)
commutator, cosocle, hypocenterC5×C72×C13C2×C3
FrattiniC1G
Fitting, socleC3×C5×C72×C13C2
LCSG ▷ C5×C72×C13
UCSC1 ◁ C3

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

Conjugacy classes & character table

4782 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×#27164943, C3×#27164944, C3×D7×D455, …
maximal normal subgroup ofC3×#27164943, C3×#27164944, C3×D7×D455, …
maximal quotient ofC3×C7⋊Dic455, C2×C3×C5⋊(C7⋊D91)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 190);