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C4×ΓL(1,𝔽8)×C43⋊C7 #38760289

order25284
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C43⋊C7
unambiguous semidirect product(C4×C7)⋊(C3×C43⋊C7)
unambiguous semidirect product(C4×ΓL(1,𝔽8)×C43)⋊C7

Splittings

FittingC4×C7×C43 ⋊ C3×C7
derivedC7×C43 ⋊ C3×C4×C7
HallC4×C7×C43⋊C7 ⋊ C3
HallC7×C43⋊C7 ⋊ C3×C4
HallC4×C43 ⋊ C7×ΓL(1,𝔽8)
SylowC43 ⋊ C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×C43⋊C7
commutator, hypocenterC7×C43C3×C4×C7
FrattiniC2C2×ΓL(1,𝔽8)×C43⋊C7
FittingC4×C7×C43C3×C7
socle, cosocleC2×C7×C43C2×C3×C7
prime radicalC2×ΓL(1,𝔽8)×C43⋊C7C2
LCSG ▷ C7×C43
UCSC1 ◁ C4

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1204

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 96);