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C11×C3⋊Dic285 #49178481

order37620
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊Dic285
unambiguous semidirect productC3⋊(C11×Dic285)
unambiguous semidirect productC19⋊(C11×C3⋊Dic15)

Splittings

derived, HallC32×C5×C19 ⋊ C4×C11
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ C3⋊Dic3
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C3⋊Dic15
HallC32×C19 ⋊ C11×Dic5
HallC32×C11 ⋊ Dic95
HallC5×C19 ⋊ C11×C3⋊Dic3
HallC5×C11 ⋊ C3⋊Dic57
HallC32×C5 ⋊ C11×Dic19
SylowC19 ⋊ C11×C3⋊Dic15
SylowC32 ⋊ C11×Dic95
SylowC5 ⋊ C11×C3⋊Dic57

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D285
commutator, hypocenterC32×C5×C19C4×C11
FrattiniC2C11×C3⋊D285
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C32×C5×C19C2×C11
LCSG ▷ C32×C5×C19
UCSC1 ◁ C2×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 190);