Finite Group Databasebeta

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C3×C5×Dic507 #44477477

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

Aliases

direct productC3×C5×Dic507
unambiguous semidirect productC3⋊(C3×C5×Dic169)

Splittings

derivedC3×C169 ⋊ C3×C4×C5
HallC32×C5×C169 ⋊ C4
HallC32×C169 ⋊ C4×C5
HallC5×C169 ⋊ C3×Dic3
SylowC169 ⋊ C3×C5×Dic3
HallC32×C5 ⋊ Dic169
SylowC32 ⋊ C5×Dic169

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D507
commutator, hypocenterC3×C169C3×C4×C5
FrattiniC2×C13C3×C5×D39
FittingC2×C32×C5×C169C2
socle, prime radicalC2×C32×C5×C13D13
cosocleC2×C3×C169C2×C3×C5
LCSG ▷ C3×C169
UCSC1 ◁ C2×C3×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10140

Conjugacy classes & character table

7650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 66);