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C2×C3×C11×C13×D7 #26046595

order12012
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×C13×D7

Splittings

Fitting, socleC2×C3×C7×C11×C13 ⋊ C2
derived, SylowC7 ⋊ C22×C3×C11×C13
HallC3×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C22×C3
HallC3×C7×C13 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C13
HallC7×C13 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C13
HallC3×C7 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13D7
commutator, cosocle, hypocenterC7C22×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2
LCSG ▷ C7
UCSC1 ◁ C2×C3×C11×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C13×D7⋊C9, C2×C11×#13109900, C2×C11×#13109901, …
maximal normal subgroup ofC2×C11×C13×D7⋊C9, C2×C11×#13109900, C2×C11×#13109901, …
maximal quotient ofC2×C9×C11×C13×D7, C3×D3×C11×C13×D7, C2×C32×C11×C13×D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 185);