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C4×C11×C7⋊(C52⋊C3) #37528382

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC4×C11×C7⋊(C52⋊C3)
unambiguous semidirect product(C4×C7)⋊(C11×C52⋊C3)
unambiguous semidirect product(C4×C52)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C4×C7×C11)⋊(C52⋊C3)
unambiguous semidirect product(C4×C52×C11)⋊ΓL(1,𝔽8)

Splittings

Fitting, HallC4×C52×C7×C11 ⋊ C3
derived, HallC52×C7 ⋊ C3×C4×C11
HallC52×C7×C11 ⋊ C3×C4
HallC4×C52×C11 ⋊ ΓL(1,𝔽8)
HallC4×C52×C7 ⋊ C3×C11
HallC4×C7×C11 ⋊ C52⋊C3
HallC52×C11 ⋊ C4×ΓL(1,𝔽8)
HallC4×C52 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C4×C52⋊C3
HallC4×C7 ⋊ C11×C52⋊C3
SylowC52 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C11C7⋊(C52⋊C3)
commutator, hypocenterC52×C7C3×C4×C11
FrattiniC2C2×C11×C7⋊(C52⋊C3)
FittingC4×C52×C7×C11C3
socleC2×C52×C7×C11C2×C3
prime radicalC2×C11×C7⋊(C52⋊C3)C2
cosocleC2×C52×C7C2×C3×C11
LCSG ▷ C52×C7
UCSC1 ◁ C4×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

2684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 193);