Finite Group Databasebeta

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C32×C5×C7×Dic19 #37561176

order23940
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C7×Dic19

Splittings

derived, SylowC19 ⋊ C32×C4×C5×C7
HallC32×C5×C7×C19 ⋊ C4
HallC32×C7×C19 ⋊ C4×C5
HallC32×C5×C19 ⋊ C4×C7
HallC5×C7×C19 ⋊ C32×C4
HallC32×C19 ⋊ C4×C5×C7
HallC7×C19 ⋊ C32×C4×C5
HallC5×C19 ⋊ C32×C4×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C7D19
commutator, hypocenterC19C32×C4×C5×C7
FrattiniC2C32×C5×C7×D19
Fitting, socle, prime radicalC2×C32×C5×C7×C19C2
cosocleC2×C19C2×C32×C5×C7
LCSG ▷ C19
UCSC1 ◁ C2×C32×C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

6930 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 308);