Finite Group Databasebeta

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C3×C5×C3⋊#63118 #26043746

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

Aliases

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

Splittings

Fitting, socle, HallC32×C52×C13 ⋊ C4
derivedC3×C5×C13 ⋊ C3×C4×C5
HallC52×C13 ⋊ C3×Dic3
HallC32×C52 ⋊ #261
HallC32×C13 ⋊ C5×Dic5
SylowC52 ⋊ C3×C3⋊#261
SylowC13 ⋊ C3×C5×Dic15
SylowC32 ⋊ C5×#63118

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#63118
commutator, hypocenterC3×C5×C13C3×C4×C5
FrattiniC1G
Fitting, socleC32×C52×C13C4
prime radicalC32×C52×D13C2
cosocleC3×C5×D13C2×C3×C5
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×C5

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

normal subgroups only

This group has 160 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 →

Conjugacy classes & character table

945 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 593);