Finite Group Databasebeta

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C5×#19154246 #44415914

order29190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#19154246

Splittings

Fitting, socle, HallC5×C7×C139 ⋊ C2×C3
derived, HallC7×C139 ⋊ C2×C3×C5
HallC5×#15668588 ⋊ C2
HallC5×C7×D139 ⋊ C3
Hall#15668588 ⋊ C2×C5
HallC7×D139 ⋊ C3×C5
HallC5×D139 ⋊ ΓL(1,𝔽8)
HallC5×C139 ⋊ C2×ΓL(1,𝔽8)
HallD139 ⋊ C5×ΓL(1,𝔽8)
SylowC139 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ D139⋊C3
SylowC7 ⋊ C5×D139⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#19154246
commutator, cosocle, hypocenterC7×C139C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C139C2×C3
LCSG ▷ C7×C139
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4865

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29190, 24);