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C2×C5×(C11⋊D11)⋊C3 #20300075

order7260
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C11

Aliases

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

Splittings

Fitting, socleC2×C5×C112 ⋊ C2×C3
derived, SylowC112 ⋊ C22×C3×C5
HallC2×C5×C11⋊D11 ⋊ C3
HallC5×C112⋊C3 ⋊ C22
HallC5×C112 ⋊ C22×C3
HallC2×C11⋊D11 ⋊ C3×C5
HallC112⋊C3 ⋊ C22×C5

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×(C11⋊D11)⋊C3, C2×C3×C5×(C11⋊D11)⋊C3, C2×C5×C3⋊((C11⋊D11)⋊C3), …
maximal normal subgroup ofC2×C3×C5×(C11⋊D11)⋊C3, C2×((C11⋊D11)⋊C3)⋊C25, C2×C25×(C11⋊D11)⋊C3, …
maximal quotient ofC2×C5×(C11⋊D11)⋊C9, C5×D3×(C11⋊D11)⋊C3, C2×C3×C5×(C11⋊D11)⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 175);