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C3×(C19⋊C3)⋊Dic7 #18012176

order4788
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C19⋊C3)⋊Dic7
unambiguous semidirect product(C19⋊C3)⋊(C3×Dic7)

Splittings

derived, HallC7×C19 ⋊ C32×C4
HallC3×C7×C19⋊C3 ⋊ C4
HallDic133 ⋊ C32
HallC3×C19⋊C3 ⋊ Dic7
SylowC19 ⋊ C32×Dic7
SylowC7 ⋊ C3×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3(C19⋊C3)⋊D7
commutator, hypocenterC7×C19C32×C4
FrattiniC2C3×(C19⋊C3)⋊D7
Fitting, socleC2×C3×C7×C19C2×C3
prime radicalC2×C3×C7×C19⋊C3C2
cosocleC2×C7×C19C2×C32
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1596

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×(C19⋊C3)⋊Dic7, C3×(C19⋊C3)⋊Dic35, C3×(C19⋊C3)⋊(C7⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC3×C5×(C19⋊C3)⋊Dic7, C3×C7×(C19⋊C3)⋊Dic7
maximal quotient ofC3×C5×(C19⋊C3)⋊Dic7, C3×(C19⋊C3)⋊Dic35, C3×(C19⋊C3)⋊(C7⋊AGL(1,𝔽5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 92);