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C5×ΓL(1,𝔽8)⋊Dic13 #19129688

order5460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊Dic13
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×Dic13)

Splittings

derived, HallC7×C13 ⋊ C3×C4×C5
HallC5×Dic91 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallDic91 ⋊ C3×C5
HallC13×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×ΓL(1,𝔽8) ⋊ Dic13
HallC5×C13 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×Dic13
HallΓL(1,𝔽8) ⋊ C5×Dic13
SylowC13 ⋊ C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C5×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D13
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)⋊D13
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

370 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)⋊(Dic13⋊C3), C3×C5×ΓL(1,𝔽8)⋊Dic13, C5×C3⋊(ΓL(1,𝔽8)⋊Dic13), …
maximal normal subgroup ofC5×ΓL(1,𝔽8)⋊(Dic13⋊C3), C3×C5×ΓL(1,𝔽8)⋊Dic13, C25×ΓL(1,𝔽8)⋊Dic13, …
maximal quotient ofC5×(C7⋊C9)⋊Dic13, C3×C5×ΓL(1,𝔽8)⋊Dic13, C5×C3⋊(ΓL(1,𝔽8)⋊Dic13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 30);