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C52⋊C3×D91 #28331644

order13650
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productC52⋊C3×D91

Splittings

Fitting, socle, derived, HallC52×C7×C13 ⋊ C2×C3
HallC7×C13×C52⋊C3 ⋊ C2
HallC52×D91 ⋊ C3
HallC13×C52⋊C3 ⋊ D7
HallC7×C52⋊C3 ⋊ D13
HallC52×C13 ⋊ C3×D7
HallC52×C7 ⋊ C3×D13
HallC7×C13 ⋊ C2×C52⋊C3
SylowC52 ⋊ C3×D91
SylowC13 ⋊ D7×C52⋊C3
SylowC7 ⋊ D13×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C13C2×C3
LCSG ▷ C52×C7×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD7×D13×C52⋊C3, #3874×D91, D91⋊#3874, …
maximal normal subgroup ofD7×D13×C52⋊C3, #3874×D91, D91⋊#3874, …
maximal quotient ofC52⋊C3×Dic91, C2×C52⋊C3×D91

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13650, 132);