Finite Group Databasebeta

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C5×C22⋊#11924776 #37561033

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

Aliases

direct productC5×C22⋊#11924776
unambiguous semidirect productC22⋊(C5×#11924776)
unambiguous semidirect product(C22×C5)⋊#11924776

Splittings

derived, HallC22×C7×C19 ⋊ C5×C9
HallC22×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C22⋊C9
HallC22×C5×C19 ⋊ C7⋊C9
HallC22×C5×C7 ⋊ #4294
HallC7×C19 ⋊ C5×C22⋊C9
HallC5×C19 ⋊ C22⋊(C7⋊C9)
HallC22×C19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C22⋊#4294
HallC22×C7 ⋊ C5×#4294
HallC22×C5 ⋊ #11924776
SylowC19 ⋊ C5×C22⋊(C7⋊C9)
SylowC7 ⋊ C5×C22⋊#4294
SylowC22 ⋊ C5×#11924776

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊#87704
commutator, hypocenterC22×C7×C19C5×C9
FrattiniC3C5×C22⋊#87704
Fitting, socle, prime radicalC22×C3×C5×C7×C19C3
cosocleC22×C3×C7×C19C3×C5
LCSG ▷ C22×C7×C19
UCSC1 ◁ C3×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 165);