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C2×C52⋊C3×C23⋊C11 #49182102

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

Aliases

direct productC2×C52⋊C3×C23⋊C11
unambiguous semidirect product(C2×C23)⋊(C11×C52⋊C3)
unambiguous semidirect product(C2×C52)⋊(C3×C23⋊C11)
unambiguous semidirect product(C2×C23×C52⋊C3)⋊C11
unambiguous semidirect product(C2×C52×C23⋊C11)⋊C3

Splittings

Fitting, socle, HallC2×C52×C23 ⋊ C3×C11
derived, HallC52×C23 ⋊ C2×C3×C11
HallC2×C52×C23⋊C11 ⋊ C3
HallC52×C23⋊C11 ⋊ C2×C3
HallC2×C23×C52⋊C3 ⋊ C11
HallC23×C52⋊C3 ⋊ C2×C11
HallC2×C52 ⋊ C3×C23⋊C11
HallC2×C23 ⋊ C11×C52⋊C3
SylowC52 ⋊ C2×C3×C23⋊C11
SylowC23 ⋊ C2×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C52⋊C3×C23⋊C11
commutator, cosocle, hypocenterC52×C23C2×C3×C11
FrattiniC1G
Fitting, socleC2×C52×C23C3×C11
LCSG ▷ C52×C23
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 39);