Finite Group Databasebeta

← Prev (#49137251) Next (#49137253) →

C5×C11×Dic3×C11⋊C5 #49137252

order36300
automorphism?
homologyAbelianization (H1) = C4×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11×Dic3×C11⋊C5
unambiguous semidirect productC3⋊(C4×C5×C11×C11⋊C5)
unambiguous semidirect product(C11×Dic3)⋊(C52×C11)
unambiguous semidirect product(C5×C11×Dic3)⋊(C5×C11)

Splittings

derivedC3×C11 ⋊ C4×C52×C11
HallC3×C5×C11×C11⋊C5 ⋊ C4
HallC112×Dic3 ⋊ C52
HallC3×C112 ⋊ C4×C52
SylowC112 ⋊ C52×Dic3
SylowC3 ⋊ C4×C5×C11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D3×C11⋊C5
commutator, hypocenterC3×C11C4×C52×C11
FrattiniC2C5×D3×C11×C11⋊C5
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C3×C11C2×C52×C11
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C11

216 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 3300

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 388);