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C11×D7×(C5⋊D5)⋊C3 #37528502

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC11×D7×(C5⋊D5)⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C22×C3
derived, HallC52×C7 ⋊ C22×C3×C11
HallC11×D7×C5⋊D5 ⋊ C3
HallC7×C11×C52⋊C3 ⋊ C22
HallC11×C52⋊C3 ⋊ C2×D7
HallD7×C5⋊D5 ⋊ C3×C11
HallC7×C52⋊C3 ⋊ C22×C11
HallC52×C11 ⋊ C2×C3×D7
HallC7×C11 ⋊ C2×(C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C2×C11×D7
SylowC52 ⋊ C2×C3×C11×D7
SylowC7 ⋊ C2×C11×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D7×(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC52×C7×C11C22×C3
LCSG ▷ C52×C7
UCSC1 ◁ C11

120 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 34 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) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 313);