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C5×ΓL(1,𝔽8)⋊Dic73 #44501267

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

Aliases

direct productC5×ΓL(1,𝔽8)⋊Dic73
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×Dic73)

Splittings

derived, HallC7×C73 ⋊ C3×C4×C5
HallC5×Dic511 ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C4
HallC5×C7×C73 ⋊ C3×C4
HallDic511 ⋊ C3×C5
HallΓL(1,𝔽8)×C73 ⋊ C4×C5
HallC5×C73 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×ΓL(1,𝔽8) ⋊ Dic73
SylowC73 ⋊ C5×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×Dic73
HallΓL(1,𝔽8) ⋊ C5×Dic73
SylowC7 ⋊ C3×C5×Dic73

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D73
commutator, hypocenterC7×C73C3×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)⋊D73
Fitting, socleC2×C5×C7×C73C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C73C2
cosocleC2×C7×C73C2×C3×C5
LCSG ▷ C7×C73
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 30);