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C3×C17×Dic5×ΓL(1,𝔽8) #36339303

order21420
automorphism?
homologyAbelianization (H1) = C32×C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×Dic5×ΓL(1,𝔽8)
unambiguous semidirect product(C7×Dic5)⋊(C32×C17)
unambiguous semidirect product(C3×C7×Dic5)⋊(C3×C17)
unambiguous semidirect product(C7×C17×Dic5)⋊C32
unambiguous semidirect product(C3×C7×C17×Dic5)⋊C3

Splittings

derived, HallC5×C7 ⋊ C32×C4×C17
HallC3×C5×C17×ΓL(1,𝔽8) ⋊ C4
HallC7×C17×Dic5 ⋊ C32
HallC5×C7×C17 ⋊ C32×C4
HallC3×C5×ΓL(1,𝔽8) ⋊ C4×C17
HallC7×Dic5 ⋊ C32×C17
HallC7×C17 ⋊ C32×Dic5
HallC5×C17 ⋊ C3×C4×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C17×Dic5
SylowC5 ⋊ C3×C4×C17×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C32×C4×C17
FrattiniC2C3×D5×C17×ΓL(1,𝔽8)
Fitting, socleC2×C3×C5×C7×C17C2×C3
prime radicalC2×C3×C5×C17×ΓL(1,𝔽8)C2
cosocleC2×C5×C7C2×C32×C17
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7140

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 135);