Finite Group Databasebeta

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C3×#13089712⋊C5 #36344964

order21780
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×#13089712⋊C5
unambiguous semidirect product#13089712⋊(C3×C5)
unambiguous semidirect product(C3×#13089712)⋊C5

Splittings

derivedC112⋊C3 ⋊ C3×C4×C5
HallC3×(C112⋊C3)⋊C5 ⋊ C4
HallC3×#13089712 ⋊ C5
HallC3×C112⋊C3 ⋊ C4×C5
Hall#10597243 ⋊ C3×Dic3
SylowC112 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C3#10624391⋊C5
commutator, hypocenterC112⋊C3C3×C4×C5
FrattiniC2C3×#10624391⋊C5
Fitting, socleC2×C3×C112C5×D3
prime radicalC2×C3×(C112⋊C3)⋊C5C2
cosocleC2×C112⋊C3C2×C3×C5
LCSG ▷ C112⋊C3
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 313);