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C9×C25×#3866 #45685751

order33300
automorphism?
homologyAbelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC9×C25×#3866

Splittings

Fitting, HallC9×C25×C37 ⋊ C4
derived, SylowC37 ⋊ C4×C9×C25
HallC25×C37 ⋊ C4×C9
HallC9×C37 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC9×C25#3866
commutator, hypocenterC37C4×C9×C25
FrattiniC3×C5C3×C5×#3866
FittingC9×C25×C37C4
socleC3×C5×C37C3×C4×C5
prime radical, cosocleC3×C5×D37C2×C3×C5
LCSG ▷ C37
UCSC1 ◁ C9×C25

54 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, 24);