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D23×#87705 #32913469

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

Aliases

direct productD23×#87705
unambiguous semidirect productC23⋊(C2×#87705)

Splittings

Fitting, socle, derived, HallC7×C19×C23 ⋊ C2×C3
HallC23×#87705 ⋊ C2
HallC7×C19×D23 ⋊ C3
HallC19×D23 ⋊ ΓL(1,𝔽8)
HallC19×C23 ⋊ C2×ΓL(1,𝔽8)
HallC7×D23 ⋊ C19⋊C3
HallC7×C23 ⋊ C2×C19⋊C3
HallC7×C19 ⋊ C3×D23
SylowC23 ⋊ C2×#87705
SylowC19 ⋊ ΓL(1,𝔽8)×D23
SylowC7 ⋊ D23×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C19×C23C2×C3
LCSG ▷ C7×C19×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3059

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD23×#11716328, D23×#11716326, D23×#11716322, …
maximal normal subgroup ofD23×#11716328, D23×#11716326, D23×#11716322, …
maximal quotient ofDic23×#87705, C2×D23×#87705

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18354, 24);