Finite Group Databasebeta

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C4×C7×C11×C52⋊C3 #37528383

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC4×C7×C11×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C3×C7×C11)
unambiguous semidirect product(C4×C52×C11)⋊(C3×C7)

Splittings

Fitting, HallC4×C52×C7×C11 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C7×C11
HallC52×C7×C11 ⋊ C3×C4
HallC4×C52×C11 ⋊ C3×C7
HallC4×C52×C7 ⋊ C3×C11
HallC52×C11 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4×C11
HallC4×C52 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC4×C7×C11C52⋊C3
commutator, hypocenterC52C3×C4×C7×C11
FrattiniC2C2×C7×C11×C52⋊C3
FittingC4×C52×C7×C11C3
socleC2×C52×C7×C11C2×C3
prime radicalC2×C7×C11×C52⋊C3C2
cosocleC2×C52C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C4×C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

3388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 194);