Finite Group Databasebeta

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C3×C5×C3⋊#10621730 #44478236

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

Aliases

direct productC3×C5×C3⋊#10621730
unambiguous semidirect productC3⋊(C3×C5×#10621730)

Splittings

Fitting, socle, HallC32×C5×C132 ⋊ C4
derivedC3×C132 ⋊ C3×C4×C5
HallC32×C132 ⋊ C4×C5
HallC5×C132 ⋊ C3×Dic3
SylowC132 ⋊ C3×C5×Dic3
HallC32×C5 ⋊ #10621730
SylowC32 ⋊ C5×#10621730

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#10621730
commutator, hypocenterC3×C132C3×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C132C4
prime radicalC32×C5×C13×D13C2
cosocleC3×C13×D13C2×C3×C5
LCSG ▷ C3×C132
UCSC1 ◁ C3×C5

148 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 780

Conjugacy classes & character table

2385 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 825);