Finite Group Databasebeta

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C3×#64525 #11744858

order912
isoclinismisoclinic class of #64525
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#64525

Splittings

FittingC3×D4×C19 ⋊ C2
HallC3×C19 ⋊ D8
SylowC19 ⋊ C3×D8

Subgroups

subgroupG/H
centerC2×C3C22⋊D19
commutator, cosocleC4×C19C22×C3
FrattiniC4C2×C3×D19
FittingC3×D4×C19C2
socleC2×C3×C19D4
hypercenterC3×D4D19
hypocenterC19C3×D8
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 456

A minimal faithful permutation representation — 2 generators on 30 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#64525, #14269397, #14269398, …
maximal normal subgroup ofD3×#64525, #14269397, #14269398, …
maximal quotient ofC3×#10597264, C3×#10597266, C3×#10597283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 69);