Finite Group Databasebeta

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C5×C3⋊#14523129 #44477828

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

Aliases

direct productC5×C3⋊#14523129
unambiguous semidirect productC3⋊(C5×#14523129)

Splittings

derivedC3×C132 ⋊ C3×C4×C5
HallC3×C5×#92789 ⋊ C4
HallC3×#92789 ⋊ C4×C5
HallC5×C132 ⋊ C3×Dic3
SylowC132 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊#11759816
commutator, hypocenterC3×C132C3×C4×C5
FrattiniC2C5×C3⋊#11759816
Fitting, socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×#92789C2
cosocleC2×C3×C132C2×C3×C5
LCSG ▷ C3×C132
UCSC1 ◁ C2×C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 417);