Finite Group Databasebeta

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C3×C5×C3⋊#10596817 #39908126

order26100
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C3⋊#10596817
unambiguous semidirect productC3⋊(C3×C5×#10596817)

Splittings

Fitting, socle, HallC32×C52×C29 ⋊ C4
derivedC3×C5×C29 ⋊ C3×C4×C5
HallC52×C29 ⋊ C3×Dic3
HallC32×C29 ⋊ C5×Dic5
HallC32×C52 ⋊ #1181
SylowC29 ⋊ C3×C5×Dic15
SylowC52 ⋊ C3×C3⋊#1181
SylowC32 ⋊ C5×#10596817

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#10596817
commutator, hypocenterC3×C5×C29C3×C4×C5
FrattiniC1G
Fitting, socleC32×C52×C29C4
prime radicalC32×C52×D29C2
cosocleC3×C5×D29C2×C3×C5
LCSG ▷ C3×C5×C29
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 →

Presentation

transitive degreeμt(G) = 870

Conjugacy classes & character table

1845 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 360);