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C23×(C19⋊C3)⋊D7 #32913486

order18354
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×(C19⋊C3)⋊D7
unambiguous semidirect product(C19⋊C3)⋊(D7×C23)

Splittings

Fitting, socle, HallC7×C19×C23 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C23
HallC7×C23×C19⋊C3 ⋊ C2
HallC23×D133 ⋊ C3
HallC23×C19⋊C3 ⋊ D7
HallC19×C23 ⋊ C3×D7
HallC7×C19⋊C3 ⋊ C2×C23
HallD133 ⋊ C3×C23
HallC7×C23 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D7×C23
SylowC19 ⋊ C3×D7×C23
SylowC7 ⋊ C23×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC23(C19⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C19C2×C3×C23
FrattiniC1G
Fitting, socleC7×C19×C23C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3059

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD23×(C19⋊C3)⋊D7, D7×C23×D19⋊C3, ((C19⋊C3)⋊D7)⋊D23, …
maximal normal subgroup ofD23×(C19⋊C3)⋊D7, D7×C23×D19⋊C3, ((C19⋊C3)⋊D7)⋊D23, …
maximal quotient ofC23×(C19⋊C3)⋊Dic7, C2×C23×(C19⋊C3)⋊D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18354, 41);