Finite Group Databasebeta

← Prev (#49151236) Next (#49151238) →

C7×C3⋊D885 #49151237

order37170
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊D885
unambiguous semidirect productC3⋊(C7×D885)
unambiguous semidirect productC5⋊(C7×C3⋊D177)
unambiguous semidirect productC59⋊(C7×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C7×C59 ⋊ C2
derived, HallC32×C5×C59 ⋊ C2×C7
HallC32×C7×C59 ⋊ D5
HallC5×C7×C59 ⋊ C3⋊D3
HallC32×C59 ⋊ C7×D5
HallC7×C59 ⋊ C3⋊D15
HallC32×C5×C7 ⋊ D59
HallC5×C59 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ D295
SylowC59 ⋊ C7×C3⋊D15
HallC32×C5 ⋊ C7×D59
HallC5×C7 ⋊ C3⋊D177
SylowC32 ⋊ C7×D295
SylowC5 ⋊ C7×C3⋊D177

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D885
commutator, cosocle, hypocenterC32×C5×C59C2×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C59C2
LCSG ▷ C32×C5×C59
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 77
transitive degreeμt(G) = 18585

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2,3,4,5,6,7)(9,10)(12,13)(15,16)(17,18)(20,21)(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)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77);(11,12,13)(14,15,17,18,16)(19,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21);(8,9,10)

Conjugacy classes & character table

9303 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37170, 62);