Finite Group Databasebeta

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C5×D3×C23×C11⋊C5 #49182124

order37950
automorphism?
homologyAbelianization (H1) = C2×C52×C23 · Schur multiplier (H2) = C5

Aliases

direct productC5×D3×C23×C11⋊C5
unambiguous semidirect productC3⋊(C2×C5×C23×C11⋊C5)
unambiguous semidirect product(D3×C11)⋊(C52×C23)
unambiguous semidirect product(C5×D3×C11)⋊(C5×C23)
unambiguous semidirect product(D3×C11×C23)⋊C52
unambiguous semidirect product(C5×D3×C11×C23)⋊C5

Splittings

Fitting, socleC3×C5×C11×C23 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C52×C23
HallC3×C5×C23×C11⋊C5 ⋊ C2
HallD3×C11×C23 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ C2×C23
HallC3×C11×C23 ⋊ C2×C52
HallC11×C23 ⋊ C52×D3
HallC3×C23 ⋊ C2×C5×C11⋊C5
HallD3×C11 ⋊ C52×C23
SylowC11 ⋊ C52×D3×C23
SylowC3 ⋊ C2×C5×C23×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5×C23D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C52×C23
FrattiniC1G
Fitting, socleC3×C5×C11×C23C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C5×C23

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

2415 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 61);