Finite Group Databasebeta

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C5×ΓL(1,𝔽8)×Dic73 #44501259

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

Aliases

direct productC5×ΓL(1,𝔽8)×Dic73

Splittings

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

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 22);