Finite Group Databasebeta

D4×Q8×Dic11 #14913641

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

Aliases

direct productD4×Q8×Dic11

Splittings

SylowC11 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×D4×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC22×D4×C11C23
hypercenterC2×D4×Q8D11
hypocenterC11C4×D4×Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×D4×Q8

3148 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, 329436);