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C22⋊#6249 #11722293

order864
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C22

Aliases

unambiguous semidirect productC22⋊#6249

Splittings

FittingC22×H(3,𝔽3) ⋊ C8
SylowH(3,𝔽3) ⋊ C22⋊C8

Subgroups

subgroupG/H
centerC2C2×#6249
commutatorC2×H(3,𝔽3)C2×C8
Frattini, socleC2×C3C2×AGL(1,𝔽9)
FittingC22×H(3,𝔽3)C8
prime radicalC22×#272C4
cosocleC2×#1088C22
hypercenterC22#6249
hypocenterH(3,𝔽3)C22⋊C8
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2 ◁ C22

107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Polycyclic presentation:

2^5,3^3|a^2=c,c^2=e,b^a=bd,f^a=f^2g^2,g^a=f^2h^2,h^a=h^2,f^c=f^2g,g^c=fgh^2,f^e=f^2,g^e=g^2h^2,g^f=gh

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13146178, #13146184, #13146444, …
maximal normal subgroup of#13146178, #13146184, #13146444, …
maximal quotient of#13146440, #13146443, #13146444, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 2260);