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C3×Dic2431 #44415717

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

Aliases

direct productC3×Dic2431
unambiguous semidirect productC11⋊(C3×Dic221)

Splittings

derived, HallC11×C13×C17 ⋊ C3×C4
HallC3×C11×C13×C17 ⋊ C4
HallC3×C13×C17 ⋊ Dic11
HallC3×C11×C17 ⋊ Dic13
HallC3×C11×C13 ⋊ Dic17
HallC13×C17 ⋊ C3×Dic11
HallC11×C17 ⋊ C3×Dic13
HallC11×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ Dic143
HallC3×C13 ⋊ Dic187
HallC3×C11 ⋊ Dic221
SylowC17 ⋊ C3×Dic143
SylowC13 ⋊ C3×Dic187
SylowC11 ⋊ C3×Dic221

Subgroups

subgroupG/H
center, hypercenterC2×C3D2431
commutator, hypocenterC11×C13×C17C3×C4
FrattiniC2C3×D2431
Fitting, socle, prime radicalC2×C3×C11×C13×C17C2
cosocleC2×C11×C13×C17C2×C3
LCSG ▷ C11×C13×C17
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29172

Conjugacy classes & character table

7302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 9);