Finite Group Databasebeta

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C4×C5×#11924777 #37560873

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

Aliases

direct productC4×C5×#11924777

Splittings

derived, HallC7×C19 ⋊ C4×C5×C9
HallC4×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C4×C9
HallC4×C7×C19 ⋊ C5×C9
HallC4×C5×C19 ⋊ C7⋊C9
HallC4×C5×C7 ⋊ #4294
HallC5×C19 ⋊ C4×C7⋊C9
HallC4×C19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C4×#4294
HallC4×C7 ⋊ C5×#4294
SylowC19 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C4×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5#87705
commutator, hypocenterC7×C19C4×C5×C9
FrattiniC2×C3C2×C5×#87705
FittingC3×C4×C5×C7×C19C3
socle, prime radicalC2×C3×C5×C7×C19C2×C3
cosocleC2×C3×C7×C19C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C3×C4×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

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, 5);