Finite Group Databasebeta

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C3×C25×#4223 #27134160

order12300
isoclinismisoclinic class of #4223
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×#4223

Splittings

Fitting, HallC3×C25×C41 ⋊ C4
derived, SylowC41 ⋊ C3×C4×C25
HallC25×C41 ⋊ C3×C4
HallC3×C41 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC3×C25#4223
commutator, hypocenterC41C3×C4×C25
FrattiniC5C3×C5×#4223
FittingC3×C25×C41C4
socleC3×C5×C41C4×C5
prime radicalC3×C5×D41C2×C5
cosocleC5×D41C2×C3×C5
LCSG ▷ C41
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C25×#4223, C32×C25×#4223, C3×C25×C3⋊#4223
maximal normal subgroup ofC9×C25×#4223, C32×C25×#4223
maximal quotient ofC9×C25×#4223, C32×C25×#4223, C3×C25×C3⋊#4223

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 22);