Finite Group Databasebeta

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Cayley diagram

C3×C22⋊D19 #90708

order456
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×C22⋊D19

Splittings

FittingC22×C3×C19 ⋊ C2
HallC3×C19 ⋊ D4
SylowC19 ⋊ C3×D4

Subgroups

subgroupG/H
centerC2×C3C2×D19
commutator, cosocleC2×C19C22×C3
FrattiniC2C2×C3×D19
FittingC22×C3×C19C2
socleC2×C3×C19C22
hypercenterC22×C3D19
hypocenterC19C3×D4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C3 ◁ C22×C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 228

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

123 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11744940, #11744941, D3×C22⋊D19, …
maximal normal subgroup of#11744940, #11744941, D3×C22⋊D19, …
maximal quotient ofC3×Dic19⋊C4, C3×(C2×D19)⋊C4, C3×#64525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 28);