Finite Group Databasebeta

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C4×C52×C79⋊C3 #37557174

order23700
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52×C79⋊C3
unambiguous semidirect product(C4×C79)⋊(C3×C52)
unambiguous semidirect product(C4×C5×C79)⋊(C3×C5)

Splittings

Fitting, HallC4×C52×C79 ⋊ C3
derived, SylowC79 ⋊ C3×C4×C52
HallC52×C79 ⋊ C3×C4
HallC4×C79 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC4×C52C79⋊C3
commutator, hypocenterC79C3×C4×C52
FrattiniC2C2×C52×C79⋊C3
FittingC4×C52×C79C3
socleC2×C52×C79C2×C3
prime radicalC2×C52×C79⋊C3C2
cosocleC2×C79C2×C3×C52
LCSG ▷ C79
UCSC1 ◁ C4×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7900

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 57);