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C5×C9×AGL(1,𝔽5)×C37 #45685997

order33300
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×AGL(1,𝔽5)×C37

Splittings

Fitting, HallC52×C9×C37 ⋊ C4
derivedC5 ⋊ C4×C5×C9×C37
HallC52×C37 ⋊ C4×C9
HallC52×C9 ⋊ C4×C37
SylowC52 ⋊ C4×C9×C37

Subgroups

subgroupG/H
center, hypercenterC5×C9×C37AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C9×C37
FrattiniC3C3×C5×AGL(1,𝔽5)×C37
FittingC52×C9×C37C4
socleC3×C52×C37C3×C4
prime radicalC3×C5×D5×C37C2×C3
cosocleC3×D5C2×C3×C5×C37
LCSG ▷ C5
UCSC1 ◁ C5×C9×C37

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6660

Conjugacy classes & character table

8325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 270);