Finite Group Databasebeta

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C4×C52⋊C3×C83 #38735226

order24900
automorphism?
homologyAbelianization (H1) = C3×C4×C83 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊C3×C83
unambiguous semidirect product(C4×C52)⋊(C3×C83)
unambiguous semidirect product(C4×C52×C83)⋊C3

Splittings

Fitting, HallC4×C52×C83 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C83
HallC52×C83 ⋊ C3×C4
HallC4×C52 ⋊ C3×C83

Subgroups

subgroupG/H
center, hypercenterC4×C83C52⋊C3
commutator, hypocenterC52C3×C4×C83
FrattiniC2C2×C52⋊C3×C83
FittingC4×C52×C83C3
socleC2×C52×C83C2×C3
prime radicalC2×C52⋊C3×C83C2
cosocleC2×C52C2×C3×C83
LCSG ▷ C52
UCSC1 ◁ C4×C83

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4980

Conjugacy classes & character table

3652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24900, 35);