Finite Group Databasebeta

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C52×C9×#3866 #45685996

order33300
automorphism?
homologyAbelianization (H1) = C4×C52×C9 · Schur multiplier (H2) = C5

Aliases

direct productC52×C9×#3866

Splittings

Fitting, HallC52×C9×C37 ⋊ C4
derived, SylowC37 ⋊ C4×C52×C9
HallC52×C37 ⋊ C4×C9
HallC9×C37 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC52×C9#3866
commutator, hypocenterC37C4×C52×C9
FrattiniC3C3×C52×#3866
FittingC52×C9×C37C4
socleC3×C52×C37C3×C4
prime radicalC3×C52×D37C2×C3
cosocleC3×D37C2×C3×C52
LCSG ▷ C37
UCSC1 ◁ C52×C9

144 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, 269);