Finite Group Databasebeta

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C3×C25×#89137 #45658188

order32700
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×#89137

Splittings

Fitting, HallC3×C25×C109 ⋊ C4
derived, SylowC109 ⋊ C3×C4×C25
HallC25×C109 ⋊ C3×C4
HallC3×C109 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC3×C25#89137
commutator, hypocenterC109C3×C4×C25
FrattiniC5C3×C5×#89137
FittingC3×C25×C109C4
socleC3×C5×C109C4×C5
prime radicalC3×C5×D109C2×C5
cosocleC5×D109C2×C3×C5
LCSG ▷ C109
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8175

Conjugacy classes & character table

2325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 24);