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C3×C25×#64408 #36346396

order21900
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×#64408

Splittings

Fitting, HallC3×C25×C73 ⋊ C4
derived, SylowC73 ⋊ C3×C4×C25
HallC25×C73 ⋊ C3×C4
HallC3×C73 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC3×C25#64408
commutator, hypocenterC73C3×C4×C25
FrattiniC5C3×C5×#64408
FittingC3×C25×C73C4
socleC3×C5×C73C4×C5
prime radicalC3×C5×D73C2×C5
cosocleC5×D73C2×C3×C5
LCSG ▷ C73
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5475

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21900, 24);