Finite Group Databasebeta

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C3×C5×Dic247 #28414722

order14820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic247

Splittings

derived, HallC13×C19 ⋊ C3×C4×C5
HallC3×C5×C13×C19 ⋊ C4
HallC5×C13×C19 ⋊ C3×C4
HallC3×C13×C19 ⋊ C4×C5
HallC3×C5×C19 ⋊ Dic13
HallC3×C5×C13 ⋊ Dic19
HallC5×C19 ⋊ C3×Dic13
HallC5×C13 ⋊ C3×Dic19
HallC3×C19 ⋊ C5×Dic13
HallC3×C13 ⋊ C5×Dic19
SylowC19 ⋊ C3×C5×Dic13
SylowC13 ⋊ C3×C5×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D247
commutator, hypocenterC13×C19C3×C4×C5
FrattiniC2C3×C5×D247
Fitting, socle, prime radicalC2×C3×C5×C13×C19C2
cosocleC2×C13×C19C2×C3×C5
LCSG ▷ C13×C19
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14820

Conjugacy classes & character table

3750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 8);