Finite Group Databasebeta

D4×C22⋊#1057 #16802977

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productD4×C22⋊#1057

Splittings

SylowC13 ⋊ D4×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C23×C8
Fitting, prime radicalC23×D4×C13C4
socleC23×C13C23×C4
cosocleC22×Dic13C24
hypercenterC23×D4#261
hypocenterC13D4×C22⋊C8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×D4

2012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1109626);