Finite Group Databasebeta

D4×C22⋊#3624 #17974382

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productD4×C22⋊#3624

Splittings

SylowC17 ⋊ D4×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C23×C8
Fitting, prime radicalC23×D4×C17C4
socleC23×C17C23×C4
cosocleC22×Dic17C24
hypercenterC23×D4#595
hypocenterC17D4×C22⋊C8
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×D4

2012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1109626);