Finite Group Databasebeta

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C3×#22547614 #37561111

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

Aliases

direct productC3×#22547614

Splittings

derived, HallC5×C7×C19 ⋊ C32×C4
HallC3×C5×#87704 ⋊ C4
HallC7×Dic95 ⋊ C32
HallC3×#87704 ⋊ Dic5
HallDic95 ⋊ C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C32×Dic5
HallC5×C19 ⋊ C3×C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C3×Dic5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×(C19⋊C3)⋊Dic5
SylowC5 ⋊ C3×#13097582

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊#11716321
commutator, hypocenterC5×C7×C19C32×C4
FrattiniC2C3×C5⋊#11716321
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×#87704C2
cosocleC2×C5×C7×C19C2×C32
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2×C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 243);