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C3×Dic1595 #34062316

order19140
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic1595
unambiguous semidirect productC11⋊(C3×Dic145)

Splittings

derived, HallC5×C11×C29 ⋊ C3×C4
HallC3×C5×C11×C29 ⋊ C4
HallC3×C11×C29 ⋊ Dic5
HallC3×C5×C29 ⋊ Dic11
HallC11×C29 ⋊ C3×Dic5
HallC3×C5×C11 ⋊ Dic29
HallC5×C29 ⋊ C3×Dic11
HallC3×C29 ⋊ Dic55
HallC5×C11 ⋊ C3×Dic29
HallC3×C11 ⋊ Dic145
SylowC29 ⋊ C3×Dic55
HallC3×C5 ⋊ Dic319
SylowC11 ⋊ C3×Dic145
SylowC5 ⋊ C3×Dic319

Subgroups

subgroupG/H
center, hypercenterC2×C3D1595
commutator, hypocenterC5×C11×C29C3×C4
FrattiniC2C3×D1595
Fitting, socle, prime radicalC2×C3×C5×C11×C29C2
cosocleC2×C5×C11×C29C2×C3
LCSG ▷ C5×C11×C29
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19140

Conjugacy classes & character table

4794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 9);