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C11⋊C5×Dic111 #37567503

order24420
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic111
unambiguous semidirect productC3⋊(C11⋊C5×Dic37)
unambiguous semidirect product(C11×Dic111)⋊C5

Splittings

derived, HallC3×C11×C37 ⋊ C4×C5
HallC3×C37×C11⋊C5 ⋊ C4
HallC11×Dic111 ⋊ C5
HallC37×C11⋊C5 ⋊ Dic3
HallC11×C37 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic37
HallC3×C37 ⋊ C4×C11⋊C5
SylowC37 ⋊ Dic3×C11⋊C5
HallC3×C11 ⋊ C5×Dic37
SylowC11 ⋊ C5×Dic111
SylowC3 ⋊ C11⋊C5×Dic37

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D111
commutator, hypocenterC3×C11×C37C4×C5
Fitting, socle, cosocleC2×C3×C11×C37C2×C5
prime radicalC2×C3×C37×C11⋊C5C2
LCSG ▷ C3×C11×C37
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4884

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 24);