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C5×C3⋊#13089712 #36345016

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

Aliases

direct productC5×C3⋊#13089712
unambiguous semidirect productC3⋊(C5×#13089712)

Splittings

derived, HallC3×C112⋊C3 ⋊ C4×C5
HallC3×C5×C112⋊C3 ⋊ C4
HallC5×C112 ⋊ C3⋊Dic3
SylowC112 ⋊ C5×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊#10624391
commutator, hypocenterC3×C112⋊C3C4×C5
FrattiniC2C5×C3⋊#10624391
Fitting, socleC2×C3×C5×C112D3
prime radicalC2×C3×C5×C112⋊C3C2
cosocleC2×C3×C112⋊C3C2×C5
LCSG ▷ C3×C112⋊C3
UCSC1 ◁ C2×C5

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

810 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 365);