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C11×(C43⋊C3)⋊Dic5 #43248784

order28380
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C43⋊C3)⋊Dic5
unambiguous semidirect product(C43⋊C3)⋊(C11×Dic5)
unambiguous semidirect productDic215⋊(C3×C11)
unambiguous semidirect product(C11×Dic215)⋊C3

Splittings

derived, HallC5×C43 ⋊ C3×C4×C11
HallC11×Dic215 ⋊ C3
HallC5×C11×C43⋊C3 ⋊ C4
HallC5×C11×C43 ⋊ C3×C4
HallC11×C43⋊C3 ⋊ Dic5
HallDic215 ⋊ C3×C11
HallC5×C43⋊C3 ⋊ C4×C11
HallC11×C43 ⋊ C3×Dic5
HallC43⋊C3 ⋊ C11×Dic5
HallC5×C11 ⋊ (C43⋊C3)⋊C4
SylowC43 ⋊ C3×C11×Dic5
SylowC5 ⋊ C11×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊(D43⋊C3)
commutator, hypocenterC5×C43C3×C4×C11
FrattiniC2C11×C5⋊(D43⋊C3)
Fitting, socleC2×C5×C11×C43C2×C3
prime radicalC2×C5×C11×C43⋊C3C2
cosocleC2×C5×C43C2×C3×C11
LCSG ▷ C5×C43
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9460

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 31);