Finite Group Databasebeta

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C3×C25×#90673 #46799875

order33900
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×#90673

Splittings

Fitting, HallC3×C25×C113 ⋊ C4
derived, SylowC113 ⋊ C3×C4×C25
HallC25×C113 ⋊ C3×C4
HallC3×C113 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC3×C25#90673
commutator, hypocenterC113C3×C4×C25
FrattiniC5C3×C5×#90673
FittingC3×C25×C113C4
socleC3×C5×C113C4×C5
prime radicalC3×C5×D113C2×C5
cosocleC5×D113C2×C3×C5
LCSG ▷ C113
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8475

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33900, 10);