Finite Group Databasebeta

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C3×C5×Dic391 #37553277

order23460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic391
unambiguous semidirect productC23⋊(C3×C5×Dic17)

Splittings

derived, HallC17×C23 ⋊ C3×C4×C5
HallC3×C5×C17×C23 ⋊ C4
HallC5×C17×C23 ⋊ C3×C4
HallC3×C17×C23 ⋊ C4×C5
HallC3×C5×C23 ⋊ Dic17
HallC3×C5×C17 ⋊ Dic23
HallC5×C23 ⋊ C3×Dic17
HallC5×C17 ⋊ C3×Dic23
HallC3×C23 ⋊ C5×Dic17
HallC3×C17 ⋊ C5×Dic23
SylowC23 ⋊ C3×C5×Dic17
SylowC17 ⋊ C3×C5×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D391
commutator, hypocenterC17×C23C3×C4×C5
FrattiniC2C3×C5×D391
Fitting, socle, prime radicalC2×C3×C5×C17×C23C2
cosocleC2×C17×C23C2×C3×C5
LCSG ▷ C17×C23
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23460

Conjugacy classes & character table

5910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 4);