Finite Group Databasebeta

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C32×C25×#3866 #45685872

order33300
automorphism?
homologyAbelianization (H1) = C32×C4×C25 · Schur multiplier (H2) = C3

Aliases

direct productC32×C25×#3866

Splittings

Fitting, HallC32×C25×C37 ⋊ C4
derived, SylowC37 ⋊ C32×C4×C25
HallC25×C37 ⋊ C32×C4
HallC32×C37 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC32×C25#3866
commutator, hypocenterC37C32×C4×C25
FrattiniC5C32×C5×#3866
FittingC32×C25×C37C4
socleC32×C5×C37C4×C5
prime radicalC32×C5×D37C2×C5
cosocleC5×D37C2×C32×C5
LCSG ▷ C37
UCSC1 ◁ C32×C25

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8325

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 145);