Finite Group Databasebeta

D59×Q8⋊C16 #28498486

order15104
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD59×Q8⋊C16

Splittings

FittingC59×Q8⋊C16 ⋊ C2
SylowC59 ⋊ C2×Q8⋊C16

Subgroups

subgroupG/H
centerC2×C8D4×D59
commutatorC4×C59C22×C16
FrattiniC4×C8C22×D59
FittingC59×Q8⋊C16C2
socleC22×C59C2×C22⋊C8
prime radicalC22×D59C22⋊C8
cosocleC4×C8×C59C23
hypercenterQ8⋊C16D59
hypocenterC59C2×Q8⋊C16
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 79365);