Finite Group Databasebeta

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C3×C5×#13097587 #37561095

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

Aliases

direct productC3×C5×#13097587

Splittings

derived, HallC7×C19 ⋊ C32×C4×C5
HallC3×C5×#87705 ⋊ C4
HallC5×C19×Dic7 ⋊ C32
HallC3×#87705 ⋊ C4×C5
HallC5×C7×C19 ⋊ C32×C4
HallC19×Dic7 ⋊ C32×C5
HallC5×Dic7 ⋊ C3×C19⋊C3
HallC5×C19 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C3×C4×C19⋊C3
HallDic7 ⋊ C3×C5×C19⋊C3
SylowC19 ⋊ C3×C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C4×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5#11716326
commutator, hypocenterC7×C19C32×C4×C5
FrattiniC2C3×C5×#11716326
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×#87705C2
cosocleC2×C7×C19C2×C32×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

1110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 227);