Finite Group Databasebeta

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C3×C5×C3⋊#11717961 #49147114

order36900
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C3⋊#11717961
unambiguous semidirect productC3⋊(C3×C5×#11717961)

Splittings

Fitting, socle, HallC32×C52×C41 ⋊ C4
derivedC3×C5×C41 ⋊ C3×C4×C5
HallC52×C41 ⋊ C3×Dic3
HallC32×C41 ⋊ C5×AGL(1,𝔽5)
HallC32×C52 ⋊ #4223
SylowC41 ⋊ C3×C5×ΓL(1,𝔽16)
SylowC52 ⋊ C3×C3⋊#4223
SylowC32 ⋊ C5×#11717961

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#11717961
commutator, hypocenterC3×C5×C41C3×C4×C5
FrattiniC1G
Fitting, socleC32×C52×C41C4
prime radicalC32×C5×D205C2
cosocleC3×D205C2×C3×C5
LCSG ▷ C3×C5×C41
UCSC1 ◁ C3×C5

124 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 2460

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(36900, 515);