Finite Group Databasebeta

← Prev (#31825366) Next (#31825368) →

Dic5×ΓL(1,𝔽8)×C43 #31825367

order18060
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1

Aliases

direct productDic5×ΓL(1,𝔽8)×C43
unambiguous semidirect product(C7×Dic5)⋊(C3×C43)

Splittings

derived, HallC5×C7 ⋊ C3×C4×C43
HallC7×Dic5×C43 ⋊ C3
HallC5×ΓL(1,𝔽8)×C43 ⋊ C4
HallC5×C7×C43 ⋊ C3×C4
HallC7×C43 ⋊ C3×Dic5
HallC5×C43 ⋊ C4×ΓL(1,𝔽8)
HallC7×Dic5 ⋊ C3×C43
HallC5×ΓL(1,𝔽8) ⋊ C4×C43
SylowC7 ⋊ C3×Dic5×C43
SylowC5 ⋊ C4×ΓL(1,𝔽8)×C43

Subgroups

subgroupG/H
center, hypercenterC2×C43D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C43
FrattiniC2D5×ΓL(1,𝔽8)×C43
Fitting, socleC2×C5×C7×C43C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C43C2
cosocleC2×C5×C7C2×C3×C43
LCSG ▷ C5×C7
UCSC1 ◁ C2×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6020

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 43);