Finite Group Databasebeta

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C4×C52×#66526 #45686087

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

Aliases

direct productC4×C52×#66526

Splittings

Fitting, HallC4×C52×C37 ⋊ C9
derived, SylowC37 ⋊ C4×C52×C9
HallC52×C37 ⋊ C4×C9
HallC4×C37 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC4×C52#66526
commutator, hypocenterC37C4×C52×C9
FrattiniC2C2×C52×#66526
FittingC4×C52×C37C9
socleC2×C52×C37C2×C9
prime radicalC2×C52×C37⋊C3C2×C3
cosocleC2×C37⋊C3C2×C3×C52
LCSG ▷ C37
UCSC1 ◁ C4×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3700

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 360);