Finite Group Databasebeta

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C3×C5×Dic527 #44539250

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic527

Splittings

derived, HallC17×C31 ⋊ C3×C4×C5
HallC3×C5×C17×C31 ⋊ C4
HallC5×C17×C31 ⋊ C3×C4
HallC3×C17×C31 ⋊ C4×C5
HallC3×C5×C31 ⋊ Dic17
HallC3×C5×C17 ⋊ Dic31
HallC5×C31 ⋊ C3×Dic17
HallC3×C31 ⋊ C5×Dic17
HallC5×C17 ⋊ C3×Dic31
HallC3×C17 ⋊ C5×Dic31
SylowC31 ⋊ C3×C5×Dic17
SylowC17 ⋊ C3×C5×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D527
commutator, hypocenterC17×C31C3×C4×C5
FrattiniC2C3×C5×D527
Fitting, socle, prime radicalC2×C3×C5×C17×C31C2
cosocleC2×C17×C31C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31620

Conjugacy classes & character table

7950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 7);