Finite Group Databasebeta

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C3×C5×C3⋊#10596814 #39908133

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

Aliases

direct productC3×C5×C3⋊#10596814
unambiguous semidirect productC3⋊(C3×C5×#10596814)

Splittings

Fitting, socle, HallC32×C52×C29 ⋊ C4
derivedC3×C5×C29 ⋊ C3×C4×C5
HallC52×C29 ⋊ C3×Dic3
HallC32×C29 ⋊ C5×AGL(1,𝔽5)
HallC32×C52 ⋊ #1181
SylowC29 ⋊ C3×C5×ΓL(1,𝔽16)
SylowC52 ⋊ C3×C3⋊#1181
SylowC32 ⋊ C5×#10596814

Subgroups

subgroupG/H
center, hypercenterC3×C5C3⋊#10596814
commutator, hypocenterC3×C5×C29C3×C4×C5
FrattiniC1G
Fitting, socleC32×C52×C29C4
prime radicalC32×C5×D145C2
cosocleC3×D145C2×C3×C5
LCSG ▷ C3×C5×C29
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) = 1740

Conjugacy classes & character table

1710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 367);