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C11×Dic555 #37567496

order24420
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic555
unambiguous semidirect productC3⋊(C11×Dic185)

Splittings

derived, HallC3×C5×C37 ⋊ C4×C11
HallC3×C5×C11×C37 ⋊ C4
HallC5×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ Dic5
HallC11×C37 ⋊ Dic15
HallC5×C37 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ Dic37
HallC3×C37 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic111
SylowC37 ⋊ C11×Dic15
HallC3×C11 ⋊ Dic185
HallC3×C5 ⋊ C11×Dic37
SylowC5 ⋊ C11×Dic111
SylowC3 ⋊ C11×Dic185

Subgroups

subgroupG/H
center, hypercenterC2×C11D555
commutator, hypocenterC3×C5×C37C4×C11
FrattiniC2C11×D555
Fitting, socle, prime radicalC2×C3×C5×C11×C37C2
cosocleC2×C3×C5×C37C2×C11
LCSG ▷ C3×C5×C37
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24420

Conjugacy classes & character table

6138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 17);