Finite Group Databasebeta

← Prev (#44501262) Next (#44501264) →

C5×C73×ΓL(1,𝔽8)⋊C4 #44501263

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C73 · Schur multiplier (H2) = C1

Aliases

direct productC5×C73×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C5×C73)
unambiguous semidirect productDic7⋊(C3×C5×C73)
unambiguous semidirect product(C5×Dic7)⋊(C3×C73)

Splittings

derived, SylowC7 ⋊ C3×C4×C5×C73
HallC5×Dic7×C73 ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C4
HallC5×C7×C73 ⋊ C3×C4
HallDic7×C73 ⋊ C3×C5
HallΓL(1,𝔽8)×C73 ⋊ C4×C5
HallC7×C73 ⋊ C3×C4×C5
HallC5×Dic7 ⋊ C3×C73
HallC5×ΓL(1,𝔽8) ⋊ C4×C73
HallC5×C7 ⋊ C3×C4×C73
HallDic7 ⋊ C3×C5×C73
HallΓL(1,𝔽8) ⋊ C4×C5×C73

Subgroups

subgroupG/H
center, hypercenterC2×C5×C73AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C5×C73
FrattiniC2C5×AGL(1,𝔽7)×C73
Fitting, socleC2×C5×C7×C73C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C73C2
cosocleC2×C7C2×C3×C5×C73
LCSG ▷ C7
UCSC1 ◁ C2×C5×C73

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

5110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 26);