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ΓL(1,𝔽8)×Dic65 #19129696

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

Aliases

direct productΓL(1,𝔽8)×Dic65

Splittings

derived, HallC5×C7×C13 ⋊ C3×C4
HallC7×Dic65 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C4
HallC13×ΓL(1,𝔽8) ⋊ Dic5
HallC5×ΓL(1,𝔽8) ⋊ Dic13
HallC7×C13 ⋊ C3×Dic5
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic13
SylowC13 ⋊ Dic5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×Dic65
SylowC5 ⋊ ΓL(1,𝔽8)×Dic13

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D65
commutator, hypocenterC5×C7×C13C3×C4
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

340 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×Dic65⋊C3, C3×ΓL(1,𝔽8)×Dic65, ΓL(1,𝔽8)×Dic195, …
maximal normal subgroup ofΓL(1,𝔽8)×Dic65⋊C3, C3×ΓL(1,𝔽8)×Dic65, C5×ΓL(1,𝔽8)×Dic65, …
maximal quotient ofC7⋊C9×Dic65, C3×ΓL(1,𝔽8)×Dic65, ΓL(1,𝔽8)×Dic195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 38);