Finite Group Databasebeta

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Q8×C22⋊#3622 #17050840

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

Aliases

direct productQ8×C22⋊#3622

Splittings

SylowC17 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D17
commutatorC22×C17C23×C8
FittingC22×C4×Q8×C17C2
socleC23×C17C23×C4
prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenterC22×C4×Q8D17
hypocenterC17Q8×C22⋊C8
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 186084);