Finite Group Databasebeta

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C5×C3⋊#14559049 #49137265

order36300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#14559049
unambiguous semidirect productC3⋊(C5×#14559049)

Splittings

derivedC3×#10597245 ⋊ C4×C5
HallC3×C5×#10597245 ⋊ C4
HallC5×#10597245 ⋊ Dic3
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C5×Dic15
SylowC3 ⋊ C5×#14559049

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊#11925890
commutator, hypocenterC3×#10597245C4×C5
FrattiniC2C5×C3⋊#11925890
Fitting, socleC2×C3×C5×C112D5
prime radicalC2×C3×C5×#10597245C2
cosocleC2×C3×#10597245C2×C5
LCSG ▷ C3×#10597245
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 26 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) = 660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 401);