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C11×C23×(C5⋊D5)⋊C3 #49182137

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C23 · Schur multiplier (H2) = C5

Aliases

direct productC11×C23×(C5⋊D5)⋊C3
unambiguous semidirect product(C5⋊D5)⋊(C3×C11×C23)
unambiguous semidirect product(C11×C5⋊D5)⋊(C3×C23)
unambiguous semidirect product(C11×C23×C5⋊D5)⋊C3

Splittings

Fitting, socle, HallC52×C11×C23 ⋊ C2×C3
derived, SylowC52 ⋊ C2×C3×C11×C23
HallC11×C23×C52⋊C3 ⋊ C2
HallC11×C23×C5⋊D5 ⋊ C3
HallC23×C52⋊C3 ⋊ C2×C11
HallC23×C5⋊D5 ⋊ C3×C11
HallC11×C52⋊C3 ⋊ C2×C23
HallC52×C23 ⋊ C2×C3×C11
HallC11×C5⋊D5 ⋊ C3×C23
HallC52×C11 ⋊ C2×C3×C23
HallC52⋊C3 ⋊ C2×C11×C23
HallC5⋊D5 ⋊ C3×C11×C23

Subgroups

subgroupG/H
center, hypercenterC11×C23(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C2×C3×C11×C23
FrattiniC1G
Fitting, socleC52×C11×C23C2×C3
LCSG ▷ C52
UCSC1 ◁ C11×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 74);