Finite Group Databasebeta

D8×C4⋊Dic59 #28607083

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD8×C4⋊Dic59

Splittings

SylowC59 ⋊ C4⋊C4×D8

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×D8×C59C2
socleC23×C59C22×D4
prime radicalC22×D8×C59C22
cosocleC22×C4×C59C24
hypercenterC2×C4×D8D59
hypocenterC59C4⋊C4×D8
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 187962);