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C13⋊C3×ΓL(1,𝔽8)⋊Dic5 #30655192

order16380
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC13⋊C3×ΓL(1,𝔽8)⋊Dic5
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic5×C13⋊C3)
unambiguous semidirect product(C13⋊C3×Dic35)⋊C3
unambiguous semidirect product(C13×ΓL(1,𝔽8)⋊Dic5)⋊C3
unambiguous semidirect product#19129701⋊C3
unambiguous semidirect product#19129702⋊C3

Splittings

derived, HallC5×C7×C13 ⋊ C32×C4
HallC5×ΓL(1,𝔽8)×C13⋊C3 ⋊ C4
HallC13×Dic35 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ Dic5
HallDic35 ⋊ C3×C13⋊C3
HallC7×C13 ⋊ C32×Dic5
HallC5×C13 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C3×ΓL(1,𝔽8)⋊Dic5
SylowC7 ⋊ C3×Dic5×C13⋊C3
SylowC5 ⋊ C13⋊C3×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7×C13C32×C4
Fitting, socle, cosocleC2×C5×C7×C13C2×C32
prime radicalC2×C5×ΓL(1,𝔽8)×C13⋊C3C2
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 242);