Finite Group Databasebeta

← Prev (#37552068) Next (#37552070) →

C3×C5×ΓL(1,𝔽8)⋊D37 #37552069

order23310
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)⋊D37
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C5×D37)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, HallC7×C37 ⋊ C2×C32×C5
HallC3×C5×ΓL(1,𝔽8)×C37 ⋊ C2
HallC5×D259 ⋊ C32
HallC3×ΓL(1,𝔽8)×C37 ⋊ C2×C5
HallC5×C7×C37 ⋊ C2×C32
HallD259 ⋊ C32×C5
HallC3×C5×ΓL(1,𝔽8) ⋊ D37
HallC5×C37 ⋊ C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C5×D37
SylowC37 ⋊ C3×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C32×D37
SylowC7 ⋊ C32×C5×D37

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D37
commutator, cosocle, hypocenterC7×C37C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C7×C37
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1455 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 88);