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C4×D11×H(5,𝔽2) #15660372

order2816
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×D11×H(5,𝔽2)

Splittings

FittingC4×C11×H(5,𝔽2) ⋊ C2
SylowC11 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C24×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC4×C11×H(5,𝔽2)C2
socle, cosocleC22×C11C26
prime radicalC2×D11×H(5,𝔽2)C2
hypercenterC4×H(5,𝔽2)D11
hypocenterC11C2×C4×H(5,𝔽2)
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

12378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076167);