Finite Group Databasebeta

← Prev (#29503237) Next (#29503239) →

Dic15×C23⋊C11 #29503238

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

Aliases

direct productDic15×C23⋊C11
unambiguous semidirect productC3⋊(Dic5×C23⋊C11)
unambiguous semidirect product(C23×Dic15)⋊C11

Splittings

derived, HallC3×C5×C23 ⋊ C4×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallC23×Dic15 ⋊ C11
HallC5×C23⋊C11 ⋊ Dic3
HallC3×C23⋊C11 ⋊ Dic5
HallC5×C23 ⋊ C11×Dic3
HallC3×C23 ⋊ C11×Dic5
SylowC23 ⋊ C11×Dic15
HallC3×C5 ⋊ C4×C23⋊C11
SylowC5 ⋊ Dic3×C23⋊C11
SylowC3 ⋊ Dic5×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D15×C23⋊C11
commutator, hypocenterC3×C5×C23C4×C11
Fitting, socle, cosocleC2×C3×C5×C23C2×C11
prime radicalC2×C3×C5×C23⋊C11C2
LCSG ▷ C3×C5×C23
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 24);