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C3×#16861482 #27134164

order12300
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#16861482

Splittings

Fitting, HallC3×C25×C41 ⋊ C4
derived, HallC25×C41 ⋊ C3×C4
HallC3×C41 ⋊ #1035
HallC3×C25 ⋊ Dic41
SylowC41 ⋊ C3×#1035
SylowC25 ⋊ C3×Dic41

Subgroups

subgroupG/H
center, hypercenterC3#16861482
commutator, hypocenterC25×C41C3×C4
FrattiniC5C3×#11717963
FittingC3×C25×C41C4
socleC3×C5×C41AGL(1,𝔽5)
prime radicalC3×C41×D25C2
cosocleC41×D25C2×C3
LCSG ▷ C25×C41
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

870 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×#16861482, C32×#16861482, C3×C3⋊#16861482
maximal normal subgroup ofC9×#16861482, C32×#16861482
maximal quotient ofC9×#16861482, C32×#16861482, C3×C3⋊#16861482

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 26);