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D52×C11×ΓL(1,𝔽8) #37528537

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productD52×C11×ΓL(1,𝔽8)
unambiguous semidirect product(C5×D5)⋊(C2×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D52)⋊(C3×C11)
unambiguous semidirect product(C7×D52×C11)⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C22×C3
derived, HallC52×C7 ⋊ C22×C3×C11
HallC7×D52×C11 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C22
HallC7×D52 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C22×C11
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×D52
SylowC52 ⋊ C22×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D52×C11

Subgroups

subgroupG/H
center, hypercenterC11D52×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC52×C7×C11C22×C3
LCSG ▷ C52×C7
UCSC1 ◁ C11

192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 348);