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C9×AGL(1,𝔽5)×C157 #43246271

order28260
automorphism?
homologyAbelianization (H1) = C4×C9×C157 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽5)×C157

Splittings

Fitting, HallC5×C9×C157 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C157
HallC5×C157 ⋊ C4×C9
HallC5×C9 ⋊ C4×C157

Subgroups

subgroupG/H
center, hypercenterC9×C157AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C157
FrattiniC3C3×AGL(1,𝔽5)×C157
FittingC5×C9×C157C4
socleC3×C5×C157C3×C4
prime radicalC3×D5×C157C2×C3
cosocleC3×D5C2×C3×C157
LCSG ▷ C5
UCSC1 ◁ C9×C157

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7065

Conjugacy classes & character table

7065 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28260, 25);