Finite Group Databasebeta

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C25×#157×C37 #45685913

order33300
automorphism?
homologyAbelianization (H1) = C4×C25×C37 · Schur multiplier (H2) = C3

Aliases

direct productC25×#157×C37

Splittings

Fitting, HallC32×C25×C37 ⋊ C4
derived, SylowC32 ⋊ C4×C25×C37
HallC32×C37 ⋊ C4×C25
HallC32×C25 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC25×C37#157
commutator, hypocenterC32C4×C25×C37
FrattiniC5C5×#157×C37
FittingC32×C25×C37C4
socleC32×C5×C37C4×C5
prime radicalC5×C3⋊D3×C37C2×C5
cosocleC5×C3⋊D3C2×C5×C37
LCSG ▷ C32
UCSC1 ◁ C25×C37

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5550

Conjugacy classes & character table

5550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 186);