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C5×ΓL(1,𝔽8)⋊#64408 #44501292

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊#64408
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×#64408)

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C3×C4
derived, HallC7×C73 ⋊ C3×C4×C5
HallC5×C7⋊#64408 ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C4
HallC7⋊#64408 ⋊ C3×C5
HallΓL(1,𝔽8)×C73 ⋊ C4×C5
HallC5×C73 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×ΓL(1,𝔽8) ⋊ #64408
SylowC73 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×#64408
HallΓL(1,𝔽8) ⋊ C5×#64408
SylowC7 ⋊ C3×C5×#64408

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊#64408
commutator, hypocenterC7×C73C3×C4×C5
FrattiniC1G
Fitting, socleC5×C7×C73C3×C4
prime radicalC5×ΓL(1,𝔽8)×D73C2
cosocleC7×D73C2×C3×C5
LCSG ▷ C7×C73
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2555

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 55);