Finite Group Databasebeta

D4×Q8×Dic17 #17194192

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×Q8×Dic17

Splittings

SylowC17 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC2×D4×Q8×C17C2
socle, cosocleC23×C17C25
prime radicalC22×D4×C17C23
hypercenterC2×D4×Q8D17
hypocenterC17C4×D4×Q8
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×D4×Q8

3148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 329436);