Finite Group Databasebeta

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C5×C3⋊((C11⋊C5)⋊Dic11) #49137260

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

Aliases

direct productC5×C3⋊((C11⋊C5)⋊Dic11)
unambiguous semidirect productC3⋊(C5×(C11⋊C5)⋊Dic11)
unambiguous semidirect product(C11⋊C5)⋊(C5×Dic33)

Splittings

derived, HallC3×C112 ⋊ C4×C52
HallC3×C5×C11×C11⋊C5 ⋊ C4
HallC5×C11×C11⋊C5 ⋊ Dic3
HallC3⋊(C11⋊Dic11) ⋊ C52
SylowC112 ⋊ C52×Dic3
SylowC3 ⋊ C5×(C11⋊C5)⋊Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊((C11⋊C5)⋊D11)
commutator, hypocenterC3×C112C4×C52
FrattiniC2C5×C3⋊((C11⋊C5)⋊D11)
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C3×C112C2×C52
LCSG ▷ C3×C112
UCSC1 ◁ C2×C5

216 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 88 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

1230 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 396);