Finite Group Databasebeta

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C52×D759 #49182157

order37950
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×D759
unambiguous semidirect productC3⋊(C52×D253)
unambiguous semidirect productC23⋊(C52×D33)

Splittings

Fitting, socle, HallC3×C52×C11×C23 ⋊ C2
derived, HallC3×C11×C23 ⋊ C2×C52
HallC52×C11×C23 ⋊ D3
HallC3×C52×C23 ⋊ D11
HallC3×C52×C11 ⋊ D23
HallC52×C23 ⋊ D33
HallC52×C11 ⋊ D69
HallC11×C23 ⋊ C52×D3
HallC3×C52 ⋊ D253
HallC3×C23 ⋊ C52×D11
HallC3×C11 ⋊ C52×D23
SylowC23 ⋊ C52×D33
SylowC11 ⋊ C52×D69
SylowC3 ⋊ C52×D253

Subgroups

subgroupG/H
center, hypercenterC52D759
commutator, cosocle, hypocenterC3×C11×C23C2×C52
FrattiniC1G
Fitting, socleC3×C52×C11×C23C2
LCSG ▷ C3×C11×C23
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18975

Conjugacy classes & character table

9525 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 94);