Finite Group Databasebeta

C22×Q8⋊#3622 #17000670

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×Q8⋊#3622

Splittings

SylowC17 ⋊ C22×Q8⋊C8

Subgroups

subgroupG/H
centerC23×C4C22⋊D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC22×C4×Q8×C17C2
socle, prime radicalC24×C17C22⋊C4
cosocleC42×C17C24
hypercenterC22×C4×Q8D17
hypocenterC17C22×Q8⋊C8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×Q8

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135914);