Finite Group Databasebeta

← Prev (#37561096) Next (#37561098) →

C3×C5×#13097582 #37561097

order23940
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×#13097582

Splittings

derived, HallC7×C19 ⋊ C32×C4×C5
HallC3×C5×#87704 ⋊ C4
HallC5×C7×Dic19 ⋊ C32
HallC3×#87704 ⋊ C4×C5
HallC5×C7×C19 ⋊ C32×C4
HallC7×Dic19 ⋊ C32×C5
HallC5×Dic19 ⋊ C3×ΓL(1,𝔽8)
HallC5×C19 ⋊ C3×C4×ΓL(1,𝔽8)
HallDic19 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C3×C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5#11716321
commutator, hypocenterC7×C19C32×C4×C5
FrattiniC2C3×C5×#11716321
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×#87704C2
cosocleC2×C7×C19C2×C32×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 229);