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Q8×C4⋊C4×D11 #14913071

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×C4⋊C4×D11

Splittings

FittingQ8×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11C2×Q8×C4⋊C4
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 328866);