Finite Group Databasebeta

← Prev (#29503234) Next (#29503236) →

C3×(C23⋊C11)⋊Dic5 #29503235

order15180
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C23⋊C11)⋊Dic5
unambiguous semidirect product(C23⋊C11)⋊(C3×Dic5)
unambiguous semidirect productDic115⋊(C3×C11)
unambiguous semidirect product(C3×Dic115)⋊C11

Splittings

derived, HallC5×C23 ⋊ C3×C4×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallC3×Dic115 ⋊ C11
HallC5×C23⋊C11 ⋊ C3×C4
HallC3×C23⋊C11 ⋊ Dic5
HallDic115 ⋊ C3×C11
HallC3×C5×C23 ⋊ C4×C11
HallC23⋊C11 ⋊ C3×Dic5
HallC3×C23 ⋊ C11×Dic5
SylowC23 ⋊ C3×C11×Dic5
HallC3×C5 ⋊ Dic23⋊C11
SylowC5 ⋊ C3×Dic23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊AGL(1,𝔽23)
commutator, hypocenterC5×C23C3×C4×C11
FrattiniC2C3×C5⋊AGL(1,𝔽23)
Fitting, socleC2×C3×C5×C23C2×C11
prime radicalC2×C3×C5×C23⋊C11C2
cosocleC2×C5×C23C2×C3×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 21);