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C4×ΓL(1,𝔽8)×C67⋊C3 #30683100

order16884
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×ΓL(1,𝔽8)×C67⋊C3
unambiguous semidirect product(C4×C7×C67⋊C3)⋊C3
unambiguous semidirect product(C4×ΓL(1,𝔽8)×C67)⋊C3
unambiguous semidirect product(C4×#13064105)⋊C3
unambiguous semidirect product(C4×#13064104)⋊C3

Splittings

Fitting, HallC4×C7×C67 ⋊ C32
derived, HallC7×C67 ⋊ C32×C4
HallC4×C67 ⋊ C3×ΓL(1,𝔽8)
SylowC67 ⋊ C3×C4×ΓL(1,𝔽8)
HallC4×C7 ⋊ C3×C67⋊C3
SylowC7 ⋊ C3×C4×C67⋊C3

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×C67⋊C3
commutator, hypocenterC7×C67C32×C4
FrattiniC2C2×ΓL(1,𝔽8)×C67⋊C3
FittingC4×C7×C67C32
socle, cosocleC2×C7×C67C2×C32
prime radicalC2×ΓL(1,𝔽8)×C67⋊C3C2
LCSG ▷ C7×C67
UCSC1 ◁ C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1876

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 69);