Finite Group Databasebeta

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C2×C5×((C11⋊D11)⋊C3)⋊C5 #49137360

order36300
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×((C11⋊D11)⋊C3)⋊C5
unambiguous semidirect product(C2×(C11⋊D11)⋊C3)⋊C52
unambiguous semidirect product(C2×C5×(C11⋊D11)⋊C3)⋊C5
unambiguous semidirect product(C2×C5×#11925892)⋊C3

Splittings

Fitting, socleC2×C5×C112 ⋊ C2×C3×C5
derived, SylowC112 ⋊ C22×C3×C52
HallC2×C5×#11925892 ⋊ C3
HallC5×(C112⋊C3)⋊C5 ⋊ C22
HallC5×#10597243 ⋊ C22×C3
HallC2×(C11⋊D11)⋊C3 ⋊ C52
HallC2×C11⋊D11 ⋊ C3×C52
HallC112⋊C3 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C5((C11⋊D11)⋊C3)⋊C5
commutator, cosocle, hypocenterC112C22×C3×C52
FrattiniC1G
Fitting, socleC2×C5×C112C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C5

320 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 330

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 496);