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C4×D3×2−1+4 #11701792

order768
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×D3×2−1+4

Splittings

FittingC3×C4×2−1+4 ⋊ C2
SylowC3 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC2×C4C24×D3
commutatorC2×C3C25×C4
FrattiniC22C25×D3
FittingC3×C4×2−1+4C2
socle, cosocleC22×C3C26
prime radicalC2×D3×2−1+4C2
hypercenterC4×2−1+4D3
hypocenterC3C2×C4×2−1+4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

11210 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, 1076173);