Finite Group Databasebeta

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C25×C31×#157 #42124449

order27900
isoclinismisoclinic class of #157
automorphism?
homologyAbelianization (H1) = C4×C25×C31 · Schur multiplier (H2) = C3

Aliases

direct productC25×C31×#157

Splittings

Fitting, HallC32×C25×C31 ⋊ C4
derived, SylowC32 ⋊ C4×C25×C31
HallC32×C31 ⋊ C4×C25
HallC32×C25 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC25×C31#157
commutator, hypocenterC32C4×C25×C31
FrattiniC5C5×C31×#157
FittingC32×C25×C31C4
socleC32×C5×C31C4×C5
prime radicalC5×C3⋊D3×C31C2×C5
cosocleC5×C3⋊D3C2×C5×C31
LCSG ▷ C32
UCSC1 ◁ C25×C31

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 196);