Finite Group Databasebeta

← Prev (#37560869) Next (#37560871) →

C4×C5×C7×#4294 #37560870

order23940
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C7×#4294

Splittings

derived, SylowC19 ⋊ C4×C5×C7×C9
HallC4×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C4×C9
HallC4×C7×C19 ⋊ C5×C9
HallC4×C5×C19 ⋊ C7×C9
HallC7×C19 ⋊ C4×C5×C9
HallC5×C19 ⋊ C4×C7×C9
HallC4×C19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C7C19⋊C3
commutator, hypocenterC19C4×C5×C7×C9
FrattiniC2×C3C2×C5×C7×C19⋊C3
FittingC3×C4×C5×C7×C19C3
socle, prime radicalC2×C3×C5×C7×C19C2×C3
cosocleC2×C3×C19C2×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C3×C4×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

3780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 2);