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C3×#20299971 #36345013

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

Aliases

direct productC3×#20299971

Splittings

derivedC5×C112⋊C3 ⋊ C3×C4
HallC3×C5×C112⋊C3 ⋊ C4
HallC3×C112⋊C3 ⋊ Dic5
HallC5×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×Dic15
SylowC5 ⋊ C3×#13089712

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊#10624391
commutator, hypocenterC5×C112⋊C3C3×C4
FrattiniC2C3×C5⋊#10624391
Fitting, socleC2×C3×C5×C112D3
prime radicalC2×C3×C5×C112⋊C3C2
cosocleC2×C5×C112⋊C3C2×C3
LCSG ▷ C5×C112⋊C3
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

744 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 362);