Finite Group Databasebeta

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C22×C3×C5×#87705 #37561628

order23940
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C5×#87705

Splittings

Fitting, socleC22×C3×C5×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C22×C32×C5
HallC22×C5×C7×C19 ⋊ C32
HallC5×C7×C19 ⋊ C22×C32
HallC22×C7×C19 ⋊ C32×C5
HallC22×C5×C19 ⋊ C3×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C3×C19⋊C3
HallC5×C19 ⋊ C22×C3×ΓL(1,𝔽8)
HallC22×C19 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22×C3×C19⋊C3
HallC22×C7 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C22×C3×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C3×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5#87705
commutator, cosocle, hypocenterC7×C19C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C7×C19C3
LCSG ▷ C7×C19
UCSC1 ◁ C22×C3×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 760);