Finite Group Databasebeta

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C3×C5×Dic3×C169 #44477476

order30420
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C169 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C169
unambiguous semidirect productC3⋊(C3×C4×C5×C169)

Splittings

derivedC3 ⋊ C3×C4×C5×C169
HallC32×C5×C169 ⋊ C4
HallC32×C169 ⋊ C4×C5
HallC32×C5 ⋊ C4×C169
SylowC32 ⋊ C4×C5×C169

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C169D3
commutator, hypocenterC3C3×C4×C5×C169
FrattiniC2×C13C3×C5×D3×C13
FittingC2×C32×C5×C169C2
socle, prime radicalC2×C32×C5×C13C2×C13
cosocleC2×C3×C13C2×C3×C5×C13
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C169

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10140

Conjugacy classes & character table

15210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 65);