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C2×C25×ΓL(1,𝔽8)⋊D13 #41031242

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×ΓL(1,𝔽8)⋊D13
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C25×D13)

Splittings

FittingC2×C7×C13×C25 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C25
HallC2×C25×D91 ⋊ C3
HallC13×ΓL(1,𝔽8)×C25 ⋊ C22
HallC7×C13×C25 ⋊ C22×C3
HallΓL(1,𝔽8)×C25 ⋊ C2×D13
HallC2×D91 ⋊ C3×C25
HallC13×C25 ⋊ C2×AGL(1,𝔽7)
HallC13×ΓL(1,𝔽8) ⋊ C22×C25
HallC7×C25 ⋊ C2×C3×D13
HallΓL(1,𝔽8) ⋊ C2×C25×D13
SylowC13 ⋊ C2×C25×AGL(1,𝔽7)
SylowC7 ⋊ C2×C3×C25×D13

Subgroups

subgroupG/H
center, hypercenterC2×C25ΓL(1,𝔽8)⋊D13
commutator, hypocenterC7×C13C22×C3×C25
FrattiniC5C2×C5×ΓL(1,𝔽8)⋊D13
FittingC2×C7×C13×C25C2×C3
socleC2×C5×C7×C13C2×C3×C5
prime radicalC2×C5×ΓL(1,𝔽8)⋊D13C5
cosocleC5×C7×C13C22×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C2×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4550

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 132);