Finite Group Databasebeta

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C5×Dic957 #34062320

order19140
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic957
unambiguous semidirect productC3⋊(C5×Dic319)

Splittings

derived, HallC3×C11×C29 ⋊ C4×C5
HallC3×C5×C11×C29 ⋊ C4
HallC5×C11×C29 ⋊ Dic3
HallC3×C5×C29 ⋊ Dic11
HallC11×C29 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ Dic29
HallC5×C29 ⋊ Dic33
HallC3×C29 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic87
HallC3×C11 ⋊ C5×Dic29
SylowC29 ⋊ C5×Dic33
HallC3×C5 ⋊ Dic319
SylowC11 ⋊ C5×Dic87
SylowC3 ⋊ C5×Dic319

Subgroups

subgroupG/H
center, hypercenterC2×C5D957
commutator, hypocenterC3×C11×C29C4×C5
FrattiniC2C5×D957
Fitting, socle, prime radicalC2×C3×C5×C11×C29C2
cosocleC2×C3×C11×C29C2×C5
LCSG ▷ C3×C11×C29
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19140

Conjugacy classes & character table

4800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 13);