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C5×ΓL(1,𝔽8)×C263 #42120290

order27615
automorphism?
homologyAbelianization (H1) = C3×C5×C263 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×C263
unambiguous semidirect productC7⋊(C3×C5×C263)
unambiguous semidirect product(C5×C7)⋊(C3×C263)
unambiguous semidirect product(C7×C263)⋊(C3×C5)
unambiguous semidirect product(C5×C7×C263)⋊C3

Splittings

Fitting, socle, HallC5×C7×C263 ⋊ C3
derived, SylowC7 ⋊ C3×C5×C263
HallC7×C263 ⋊ C3×C5
HallC5×C7 ⋊ C3×C263

Subgroups

subgroupG/H
center, hypercenterC5×C263ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C5×C263
FrattiniC1G
Fitting, socleC5×C7×C263C3
LCSG ▷ C7
UCSC1 ◁ C5×C263

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9205

Conjugacy classes & character table

6575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27615, 2);