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C3×(Dic71⋊C5)⋊C7 #44447148

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×(Dic71⋊C5)⋊C7
unambiguous semidirect product(Dic71⋊C5)⋊(C3×C7)
unambiguous semidirect product(Dic71⋊C7)⋊(C3×C5)
unambiguous semidirect product((C71⋊C5)⋊C7)⋊(C3×C4)
unambiguous semidirect product(C3×Dic71⋊C5)⋊C7
unambiguous semidirect product(C3×Dic71⋊C7)⋊C5

Splittings

derived, SylowC71 ⋊ C3×C4×C5×C7
HallC3×(C71⋊C5)⋊C7 ⋊ C4
HallC3×Dic71⋊C7 ⋊ C5
HallC3×Dic71⋊C5 ⋊ C7
Hall(C71⋊C5)⋊C7 ⋊ C3×C4
HallDic71⋊C7 ⋊ C3×C5
HallC3×C71⋊C7 ⋊ C4×C5
HallDic71⋊C5 ⋊ C3×C7
HallC3×C71⋊C5 ⋊ C4×C7
HallC3×Dic71 ⋊ C5×C7
HallC71⋊C7 ⋊ C3×C4×C5
HallC71⋊C5 ⋊ C3×C4×C7
HallDic71 ⋊ C3×C5×C7
HallC3×C71 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽71)
commutator, hypocenterC71C3×C4×C5×C7
FrattiniC2C3×AGL(1,𝔽71)
Fitting, socleC2×C3×C71C2×C5×C7
prime radicalC2×C3×(C71⋊C5)⋊C7C2
cosocleC2×C71C2×C3×C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 852

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 36);