Finite Group Databasebeta

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C3×Dic1235 #28414726

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

Aliases

direct productC3×Dic1235

Splittings

derived, HallC5×C13×C19 ⋊ C3×C4
HallC3×C5×C13×C19 ⋊ C4
HallC3×C13×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ Dic13
HallC13×C19 ⋊ C3×Dic5
HallC3×C5×C13 ⋊ Dic19
HallC5×C19 ⋊ C3×Dic13
HallC5×C13 ⋊ C3×Dic19
HallC3×C19 ⋊ Dic65
HallC3×C13 ⋊ Dic95
SylowC19 ⋊ C3×Dic65
HallC3×C5 ⋊ Dic247
SylowC13 ⋊ C3×Dic95
SylowC5 ⋊ C3×Dic247

Subgroups

subgroupG/H
center, hypercenterC2×C3D1235
commutator, hypocenterC5×C13×C19C3×C4
FrattiniC2C3×D1235
Fitting, socle, prime radicalC2×C3×C5×C13×C19C2
cosocleC2×C5×C13×C19C2×C3
LCSG ▷ C5×C13×C19
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14820

Conjugacy classes & character table

3714 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 12);