Finite Group Databasebeta

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C3×C5×C13×Dic13⋊C3 #44477806

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C13×Dic13⋊C3
unambiguous semidirect productDic13⋊(C32×C5×C13)
unambiguous semidirect product(C3×Dic13)⋊(C3×C5×C13)
unambiguous semidirect product(C5×Dic13)⋊(C32×C13)
unambiguous semidirect product(C3×C5×Dic13)⋊(C3×C13)

Splittings

derivedC13 ⋊ C32×C4×C5×C13
HallC3×C5×C13×C13⋊C3 ⋊ C4
HallC5×C13×Dic13 ⋊ C32
HallC3×C13×C13⋊C3 ⋊ C4×C5
HallC5×C132 ⋊ C32×C4
HallC13×Dic13 ⋊ C32×C5
SylowC132 ⋊ C32×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C13D13⋊C3
commutator, hypocenterC13C32×C4×C5×C13
FrattiniC2C3×C5×C13×D13⋊C3
Fitting, socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×C13×C13⋊C3C2
cosocleC2×C13C2×C32×C5×C13
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C13

160 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

3120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 395);