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C3⋊C8×H(5,𝔽2) #11660846

order768
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC3⋊C8×H(5,𝔽2)

Splittings

SylowC3 ⋊ C8×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D3
commutatorC2×C3C24×C8
FittingC3×C4×H(5,𝔽2)C2
socleC22×C3C24×C4
prime radicalC2×C3×H(5,𝔽2)C4
cosocleC2×C3×C4C25
hypercenterC4×H(5,𝔽2)D3
hypocenterC3C8×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

2422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1035227);