Finite Group Databasebeta

← Prev (#49137265) Next (#49137267) →

C11×C3⋊((C11⋊C5)⋊Dic5) #49137266

order36300
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊((C11⋊C5)⋊Dic5)
unambiguous semidirect productC3⋊(C11×(C11⋊C5)⋊Dic5)
unambiguous semidirect product(C11⋊C5)⋊(C11×Dic15)
unambiguous semidirect productDic165⋊(C5×C11)

Splittings

derivedC3×C5×C11 ⋊ C4×C5×C11
HallC3×C5×C11×C11⋊C5 ⋊ C4
HallC5×C11×C11⋊C5 ⋊ Dic3
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C5×Dic15
SylowC3 ⋊ C11×(C11⋊C5)⋊Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊AGL(1,𝔽11))
commutator, hypocenterC3×C5×C11C4×C5×C11
FrattiniC2C11×C3⋊(C5⋊AGL(1,𝔽11))
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C3×C5×C11C2×C5×C11
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C11

136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 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

1320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 402);