Finite Group Databasebeta

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C2×2−1+4×Dic11 #15660383

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

Aliases

direct productC2×2−1+4×Dic11

Splittings

SylowC11 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC23C24×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
Fitting, prime radicalC22×C11×2−1+4C2
socleC23×C11C25
cosocleC22×C11C26
hypercenterC22×2−1+4D11
hypocenterC11C2×C4×2−1+4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 1076178);