Finite Group Databasebeta

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C3×C7×(C79⋊C3)⋊C4 #34092609

order19908
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×(C79⋊C3)⋊C4
unambiguous semidirect product(C79⋊C3)⋊(C3×C4×C7)
unambiguous semidirect productDic79⋊(C32×C7)
unambiguous semidirect product(C3×Dic79)⋊(C3×C7)

Splittings

derived, SylowC79 ⋊ C32×C4×C7
HallC3×C7×C79⋊C3 ⋊ C4
HallC7×Dic79 ⋊ C32
HallC3×C79⋊C3 ⋊ C4×C7
HallC7×C79 ⋊ C32×C4
HallDic79 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D79⋊C3
commutator, hypocenterC79C32×C4×C7
FrattiniC2C3×C7×D79⋊C3
Fitting, socleC2×C3×C7×C79C2×C3
prime radicalC2×C3×C7×C79⋊C3C2
cosocleC2×C79C2×C32×C7
LCSG ▷ C79
UCSC1 ◁ C2×C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6636

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19908, 70);