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C13×Dic5×ΓL(1,𝔽8) #19129692

order5460
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic5×ΓL(1,𝔽8)
unambiguous semidirect product(C7×Dic5)⋊(C3×C13)

Splittings

derived, HallC5×C7 ⋊ C3×C4×C13
HallC7×C13×Dic5 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC7×Dic5 ⋊ C3×C13
HallC5×ΓL(1,𝔽8) ⋊ C4×C13
HallC7×C13 ⋊ C3×Dic5
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×Dic5
SylowC5 ⋊ C4×C13×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C13D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C13
FrattiniC2D5×C13×ΓL(1,𝔽8)
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×ΓL(1,𝔽8)×C13⋊C3, C3×C13×Dic5×ΓL(1,𝔽8), C13×ΓL(1,𝔽8)×Dic15, …
maximal normal subgroup ofDic5×ΓL(1,𝔽8)×C13⋊C3, C3×C13×Dic5×ΓL(1,𝔽8), C5×C13×Dic5×ΓL(1,𝔽8), …
maximal quotient ofC13×Dic5×C7⋊C9, C3×C13×Dic5×ΓL(1,𝔽8), C13×ΓL(1,𝔽8)×Dic15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 34);