Finite Group Databasebeta

C22×D4⋊#3624 #17964684

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

Aliases

direct productC22×D4⋊#3624

Splittings

SylowC17 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC24C22⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
Fitting, prime radicalC23×D4×C17C4
socleC24×C17C22⋊C4
cosocleC4×Dic17C24
hypercenterC23×D4#595
hypocenterC17C22×D4⋊C8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D4

1886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1099928);