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C5×C7×ΓL(1,𝔽8)×D13 #34062066

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×ΓL(1,𝔽8)×D13

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC7×C13 ⋊ C2×C3×C5×C7
HallC5×C7×C13×ΓL(1,𝔽8) ⋊ C2
HallC5×C72×D13 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC72×D13 ⋊ C3×C5
HallC72×C13 ⋊ C2×C3×C5
HallC5×C72 ⋊ C3×D13
HallC5×C13 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C5×D13
SylowC13 ⋊ C2×C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5×C7ΓL(1,𝔽8)×D13
commutator, cosocle, hypocenterC7×C13C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×ΓL(1,𝔽8)×#261, C5×C7×ΓL(1,𝔽8)⋊#261, C5×C7×D13×AGL(1,𝔽7), …
maximal normal subgroup ofC5×C7×ΓL(1,𝔽8)×#261, C5×C7×ΓL(1,𝔽8)⋊#261, C5×C7×D13×AGL(1,𝔽7), …
maximal quotient ofC5×C7×ΓL(1,𝔽8)×Dic13, C2×C5×C7×ΓL(1,𝔽8)×D13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 59);