Finite Group Databasebeta

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C5×C7×C19⋊#157 #37561498

order23940
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C19⋊#157
unambiguous semidirect productC19⋊(C5×C7×#157)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC32×C19 ⋊ C4×C5×C7
HallC32×C7×C19 ⋊ C4×C5
HallC32×C5×C19 ⋊ C4×C7
HallC5×C7×C19 ⋊ #157
HallC32×C5×C7 ⋊ Dic19
HallC7×C19 ⋊ C5×#157
HallC5×C19 ⋊ C7×#157
HallC32×C7 ⋊ C5×Dic19
HallC32×C5 ⋊ C7×Dic19
SylowC19 ⋊ C5×C7×#157
SylowC32 ⋊ C5×C7×Dic19

Subgroups

subgroupG/H
center, hypercenterC5×C7C19⋊#157
commutator, hypocenterC32×C19C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC5×C7×C3⋊D3×C19C2
cosocleC3⋊D3×C19C2×C5×C7
LCSG ▷ C32×C19
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3990

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 630);