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C5×ΓL(1,𝔽8)×Dic19 #22547597

order7980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×Dic19

Splittings

derived, HallC7×C19 ⋊ C3×C4×C5
HallC5×C7×Dic19 ⋊ C3
HallC5×C19×ΓL(1,𝔽8) ⋊ C4
HallC5×C7×C19 ⋊ C3×C4
HallC7×Dic19 ⋊ C3×C5
HallC19×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×C19 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic19
SylowC19 ⋊ C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×D19
commutator, hypocenterC7×C19C3×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)×D19
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

550 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)×(C19⋊C3)⋊C4, C3×C5×ΓL(1,𝔽8)×Dic19, C5×ΓL(1,𝔽8)×Dic57
maximal normal subgroup ofC5×ΓL(1,𝔽8)×(C19⋊C3)⋊C4, C3×C5×ΓL(1,𝔽8)×Dic19
maximal quotient ofC5×C7⋊C9×Dic19, C3×C5×ΓL(1,𝔽8)×Dic19, C5×ΓL(1,𝔽8)×Dic57

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 22);