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C11⋊C5×Dic105 #37528351

order23100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic105
unambiguous semidirect productC3⋊(C11⋊C5×Dic35)
unambiguous semidirect productC7⋊(C11⋊C5×Dic15)
unambiguous semidirect product(C11×Dic105)⋊C5

Splittings

derivedC3×C5×C7×C11 ⋊ C4×C5
HallC3×C5×C7×C11⋊C5 ⋊ C4
HallC5×C7×C11⋊C5 ⋊ Dic3
HallC3×C5×C11⋊C5 ⋊ Dic7
HallC5×C11⋊C5 ⋊ Dic21
HallC3×C7×C11 ⋊ C5×Dic5
HallC7×C11 ⋊ C5×Dic15
HallC3×C11 ⋊ C5×Dic35
HallC3×C7 ⋊ Dic5×C11⋊C5
SylowC11 ⋊ C5×Dic105
SylowC7 ⋊ C11⋊C5×Dic15
SylowC3 ⋊ C11⋊C5×Dic35

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D105
commutator, hypocenterC3×C5×C7×C11C4×C5
Fitting, socle, cosocleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C2

128 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 162);