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C7×((C43⋊C3)⋊C4)⋊C7 #38760274

order25284
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC7×((C43⋊C3)⋊C4)⋊C7
unambiguous semidirect product((C43⋊C3)⋊C4)⋊C72
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C4×C7)
unambiguous semidirect product(Dic43⋊C7)⋊(C3×C7)
unambiguous semidirect product(C7×(C43⋊C3)⋊C4)⋊C7

Splittings

derived, SylowC43 ⋊ C3×C4×C72
HallC7×Dic43⋊C7 ⋊ C3
HallC7×(C43⋊C3)⋊C7 ⋊ C4
HallC7×C43⋊C7 ⋊ C3×C4
Hall(C43⋊C3)⋊C4 ⋊ C72
HallDic43 ⋊ C3×C72
HallC43⋊C3 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC2×C7AGL(1,𝔽43)
commutator, hypocenterC43C3×C4×C72
FrattiniC2C7×AGL(1,𝔽43)
Fitting, socleC2×C7×C43C2×C3×C7
prime radicalC2×C7×(C43⋊C3)⋊C7C2
cosocleC2×C43C2×C3×C72
LCSG ▷ C43
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1204

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 81);