Finite Group Databasebeta

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C5×C3⋊(#63118⋊C3) #26043611

order11700
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(#63118⋊C3)
unambiguous semidirect productC3⋊(C5×#63118⋊C3)
unambiguous semidirect product(C3⋊#63118)⋊(C3×C5)
unambiguous semidirect product(C5×C3⋊#63118)⋊C3

Splittings

Fitting, socleC3×C52×C13 ⋊ C3×C4
derivedC3×C5×C13 ⋊ C3×C4×C5
HallC3×C52×C13⋊C3 ⋊ C4
HallC52×C13 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C5×Dic5
SylowC52 ⋊ C3⋊AGL(1,𝔽13)
SylowC13 ⋊ C3×C5×Dic15

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(#63118⋊C3)
commutator, hypocenterC3×C5×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C52×C13C3×C4
prime radicalC3×C52×D13⋊C3C2
cosocleC3×C5×D13C2×C3×C5
LCSG ▷ C3×C5×C13
UCSC1 ◁ C5

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

normal subgroups only

This group has 160 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 →

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 458);