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C3×C17×Dic143 #44415716

order29172
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic143
unambiguous semidirect productC11⋊(C3×C17×Dic13)

Splittings

derived, HallC11×C13 ⋊ C3×C4×C17
HallC3×C11×C13×C17 ⋊ C4
HallC11×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ Dic11
HallC3×C11×C17 ⋊ Dic13
HallC3×C11×C13 ⋊ C4×C17
HallC13×C17 ⋊ C3×Dic11
HallC11×C17 ⋊ C3×Dic13
HallC3×C13 ⋊ C17×Dic11
HallC3×C11 ⋊ C17×Dic13
SylowC13 ⋊ C3×C17×Dic11
SylowC11 ⋊ C3×C17×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D143
commutator, hypocenterC11×C13C3×C4×C17
FrattiniC2C3×C17×D143
Fitting, socle, prime radicalC2×C3×C11×C13×C17C2
cosocleC2×C11×C13C2×C3×C17
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29172

Conjugacy classes & character table

7446 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 8);