Finite Group Databasebeta

← Prev (#34093034) Next (#34093036) →

C5×D5×#87705 #34093035

order19950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D5×#87705
unambiguous semidirect productC5⋊(C2×C5×#87705)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C2×C3
derivedC5×C7×C19 ⋊ C2×C3×C5
HallC52×#87705 ⋊ C2
HallC5×C7×D5×C19 ⋊ C3
HallC5×D5×C19 ⋊ ΓL(1,𝔽8)
HallC52×C19 ⋊ C2×ΓL(1,𝔽8)
HallC5×C7×D5 ⋊ C19⋊C3
HallC52×C7 ⋊ C2×C19⋊C3
HallC7×C19 ⋊ C3×C5×D5
SylowC52 ⋊ C2×#87705
SylowC19 ⋊ C5×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C5×D5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D5×#87705
commutator, cosocle, hypocenterC5×C7×C19C2×C3×C5
FrattiniC1G
Fitting, socleC52×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19950, 74);