Finite Group Databasebeta

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C25×#157×C41 #49146752

order36900
automorphism?
homologyAbelianization (H1) = C4×C25×C41 · Schur multiplier (H2) = C3

Aliases

direct productC25×#157×C41

Splittings

Fitting, HallC32×C25×C41 ⋊ C4
derived, SylowC32 ⋊ C4×C25×C41
HallC32×C41 ⋊ C4×C25
HallC32×C25 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC25×C41#157
commutator, hypocenterC32C4×C25×C41
FrattiniC5C5×#157×C41
FittingC32×C25×C41C4
socleC32×C5×C41C4×C5
prime radicalC5×C3⋊D3×C41C2×C5
cosocleC5×C3⋊D3C2×C5×C41
LCSG ▷ C32
UCSC1 ◁ C25×C41

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6150

Conjugacy classes & character table

6150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 153);