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C3×Dic2035 #37567490

order24420
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic2035
unambiguous semidirect productC11⋊(C3×Dic185)

Splittings

derived, HallC5×C11×C37 ⋊ C3×C4
HallC3×C5×C11×C37 ⋊ C4
HallC3×C11×C37 ⋊ Dic5
HallC3×C5×C37 ⋊ Dic11
HallC11×C37 ⋊ C3×Dic5
HallC5×C37 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic37
HallC3×C37 ⋊ Dic55
HallC5×C11 ⋊ C3×Dic37
SylowC37 ⋊ C3×Dic55
HallC3×C11 ⋊ Dic185
HallC3×C5 ⋊ Dic407
SylowC11 ⋊ C3×Dic185
SylowC5 ⋊ C3×Dic407

Subgroups

subgroupG/H
center, hypercenterC2×C3D2035
commutator, hypocenterC5×C11×C37C3×C4
FrattiniC2C3×D2035
Fitting, socle, prime radicalC2×C3×C5×C11×C37C2
cosocleC2×C5×C11×C37C2×C3
LCSG ▷ C5×C11×C37
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24420

Conjugacy classes & character table

6114 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 11);