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C52×C13×C22⋊ΓL(1,𝔽8) #41032080

order27300
automorphism?
homologyAbelianization (H1) = C3×C52×C13 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C13×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C52×C13×ΓL(1,𝔽8))
unambiguous semidirect productC7⋊(C52×A4×C13)
unambiguous semidirect product(C22×C5)⋊(C5×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C5×C7)⋊(C5×A4×C13)

Splittings

Fitting, socle, HallC22×C52×C7×C13 ⋊ C3
derived, HallC22×C7 ⋊ C3×C52×C13
HallC52×C7×C13 ⋊ A4
HallC22×C52×C13 ⋊ ΓL(1,𝔽8)
HallC22×C52×C7 ⋊ C3×C13
HallC22×C7×C13 ⋊ C3×C52
HallC52×C7 ⋊ A4×C13
HallC22×C52 ⋊ C13×ΓL(1,𝔽8)
HallC7×C13 ⋊ C52×A4
HallC22×C13 ⋊ C52×ΓL(1,𝔽8)
SylowC7 ⋊ C52×A4×C13
SylowC22 ⋊ C52×C13×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC52×C13C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C52×C13
FrattiniC1G
Fitting, socleC22×C52×C7×C13C3
LCSG ▷ C22×C7
UCSC1 ◁ C52×C13

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9100

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 970);