Finite Group Databasebeta

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C2×C5×D7×#4296 #37561233

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D7×#4296

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C9
derived, HallC7×C19 ⋊ C22×C5×C9
HallC5×C7×#4296 ⋊ C22
HallC2×C5×D7×C19 ⋊ C9
HallC7×#4296 ⋊ C22×C5
HallC5×C7×C19 ⋊ C22×C9
HallC2×D7×C19 ⋊ C5×C9
HallC5×C19 ⋊ C2×C9×D7
HallC5×C7 ⋊ C22×#4296
SylowC19 ⋊ C2×C5×C9×D7
SylowC7 ⋊ C22×C5×#4296

Subgroups

subgroupG/H
center, hypercenterC2×C5D7×#4296
commutator, hypocenterC7×C19C22×C5×C9
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C9
prime radicalC2×C5×D7×C19⋊C3C3
cosocleC7×C19⋊C3C22×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 365);