Finite Group Databasebeta

← Prev (#34093104) Next (#34093106) →

C7×C3⋊(C5⋊D95) #34093105

order19950
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×C3⋊(C5⋊D95)
unambiguous semidirect productC3⋊(C7×C5⋊D95)
unambiguous semidirect productC5⋊(C7×D285)
unambiguous semidirect productC19⋊(C7×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C7×C19 ⋊ C2
derived, HallC3×C52×C19 ⋊ C2×C7
HallC52×C7×C19 ⋊ D3
HallC3×C52×C7 ⋊ D19
HallC52×C19 ⋊ D3×C7
HallC3×C7×C19 ⋊ C5⋊D5
HallC52×C7 ⋊ D57
HallC7×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C7×D19
HallC3×C19 ⋊ C7×C5⋊D5
SylowC52 ⋊ C7×D57
HallC3×C7 ⋊ C5⋊D95
SylowC19 ⋊ C7×C3⋊(C5⋊D5)
SylowC3 ⋊ C7×C5⋊D95

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C5⋊D95)
commutator, cosocle, hypocenterC3×C52×C19C2×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C19C2
LCSG ▷ C3×C52×C19
UCSC1 ◁ C7

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 9975

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

4998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 144);