Finite Group Databasebeta

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C5×C3⋊(#10625194⋊C3) #45686285

order33300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(#10625194⋊C3)
unambiguous semidirect productC3⋊(C5×#10625194⋊C3)
unambiguous semidirect product(C3⋊#10625194)⋊(C3×C5)
unambiguous semidirect product(C5×C3⋊#10625194)⋊C3

Splittings

Fitting, socleC3×C52×C37 ⋊ C3×C4
derivedC3×C5×C37 ⋊ C3×C4×C5
HallC3×C52×C37⋊C3 ⋊ C4
HallC52×C37 ⋊ C3×Dic3
HallC3×C37⋊C3 ⋊ C5×Dic5
SylowC37 ⋊ C3×C5×Dic15
SylowC52 ⋊ C3⋊(#3866⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(#10625194⋊C3)
commutator, hypocenterC3×C5×C37C3×C4×C5
FrattiniC1G
Fitting, socleC3×C52×C37C3×C4
prime radicalC3×C52×D37⋊C3C2
cosocleC3×C5×D37C2×C3×C5
LCSG ▷ C3×C5×C37
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 →

Presentation

transitive degreeμt(G) = 1110

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 558);