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C3⋊(C5⋊D5)×C23⋊C11 #49182113

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

Aliases

direct productC3⋊(C5⋊D5)×C23⋊C11
unambiguous semidirect productC3⋊(C5⋊D5×C23⋊C11)
unambiguous semidirect productC5⋊(D15×C23⋊C11)
unambiguous semidirect product(C23×C3⋊(C5⋊D5))⋊C11

Splittings

Fitting, socle, derived, HallC3×C52×C23 ⋊ C2×C11
HallC3×C52×C23⋊C11 ⋊ C2
HallC52×C23⋊C11 ⋊ D3
HallC23×C3⋊(C5⋊D5) ⋊ C11
HallC3×C23⋊C11 ⋊ C5⋊D5
HallC52×C23 ⋊ D3×C11
HallC3×C52 ⋊ C2×C23⋊C11
HallC3×C23 ⋊ C11×C5⋊D5
SylowC52 ⋊ D3×C23⋊C11
SylowC23 ⋊ C11×C3⋊(C5⋊D5)
SylowC3 ⋊ C5⋊D5×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C23C2×C11
LCSG ▷ C3×C52×C23
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1725

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 50);