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C7×C3⋊((C19⋊C3)⋊C4) #18012178

order4788
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊((C19⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C7×(C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(C7×Dic3)
unambiguous semidirect productDic57⋊(C3×C7)

Splittings

derivedC3×C19 ⋊ C3×C4×C7
HallC3×C7×C19⋊C3 ⋊ C4
HallC3×C19⋊C3 ⋊ C4×C7
HallC7×C19 ⋊ C3×Dic3
SylowC19 ⋊ C3×C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(D19⋊C3)
commutator, hypocenterC3×C19C3×C4×C7
FrattiniC2C7×C3⋊(D19⋊C3)
Fitting, socleC2×C3×C7×C19C2×C3
prime radicalC2×C3×C7×C19⋊C3C2
cosocleC2×C3×C19C2×C3×C7
LCSG ▷ C3×C19
UCSC1 ◁ C2×C7

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1596

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×C3⋊((C19⋊C3)⋊C4), C7×C3⋊((C19⋊C3)⋊Dic5), C7×C3⋊((C19⋊C3)⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC5×C7×C3⋊((C19⋊C3)⋊C4), C49×C3⋊((C19⋊C3)⋊C4), C72×C3⋊((C19⋊C3)⋊C4)
maximal quotient ofC5×C7×C3⋊((C19⋊C3)⋊C4), C7×C3⋊((C19⋊C3)⋊Dic5), C7×C3⋊((C19⋊C3)⋊AGL(1,𝔽5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 94);