Finite Group Databasebeta

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C22×C5×C7×#4296 #37561433

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C7×#4296

Splittings

Fitting, socle, HallC22×C5×C7×C19 ⋊ C9
derived, SylowC19 ⋊ C22×C5×C7×C9
HallC5×C7×C19 ⋊ C22×C9
HallC22×C7×C19 ⋊ C5×C9
HallC22×C5×C19 ⋊ C7×C9
HallC7×C19 ⋊ C22×C5×C9
HallC5×C19 ⋊ C22×C7×C9
HallC22×C19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC22×C5×C7#4296
commutator, hypocenterC19C22×C5×C7×C9
FrattiniC1G
Fitting, socleC22×C5×C7×C19C9
prime radicalC22×C5×C7×C19⋊C3C3
cosocleC19⋊C3C22×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C22×C5×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2660

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 565);