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C3×#16861483 #27134165

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

Aliases

direct productC3×#16861483

Splittings

Fitting, HallC3×C25×C41 ⋊ C4
derived, HallC25×C41 ⋊ C3×C4
HallC3×C41 ⋊ Dic25
HallC3×C25 ⋊ #4223
SylowC41 ⋊ C3×Dic25
SylowC25 ⋊ C3×#4223

Subgroups

subgroupG/H
center, hypercenterC3#16861483
commutator, hypocenterC25×C41C3×C4
FrattiniC5C3×#11717964
FittingC3×C25×C41C4
socleC3×C5×C41Dic5
prime radicalC3×C5×D41D5
cosocleC25×D41C2×C3
LCSG ▷ C25×C41
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

834 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×#16861483, C32×#16861483, C3×C3⋊#16861483
maximal normal subgroup ofC9×#16861483, C32×#16861483
maximal quotient ofC9×#16861483, C32×#16861483, C3×C3⋊#16861483

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 27);